Earthquake loss and risk estimation of buildings by Monte Carlo simulation

The methodology of earthquake loss and risk estimation using Monte Carlo simulation has been developed to predict probabilistic risks of buildings subject to ground motion hazard, under two different assumptions including: (1) assuming at most one earthquake in a time window; (2) assuming an arbitrary number of earthquakes in a time window. Under the first assumption, the loss exceedance probability is obtained by integrating loss distributions conditioned on various earthquake intensity levels, which are simulated by using fragility curves, with the hazard curve. The simulation is then extended to adjacent buildings with damage correlation modeled by prescribed correlation functions, and to non-adjacent buildings subject to uncorrelated ground motions. Under the second assumption, multiple earthquakes in a time window are modeled as a Poisson arrival process with different scenario intensities. The seismic performance variable of a single building, in terms of maximum interstory drift ratio or aggregate loss, is simulated based on the building's fragility curves and the intensity of each earthquake scenario. Individual and overall fragility curves are developed and applied to the simulation, in order to account for non-ergodic and ergodic structural behaviors, respectively. The methodology is finally extended to estimate the aggregate loss of multiple adjacent buildings, accounting for interactive effects from structural and/or damage correlation in one event, and from structural non-ergodicity in time. Only general directions are provided for estimating the aggregate loss of multiple buildings over multiple earthquake events by using individual and/or overall fragility curves. The major innovations of this thesis are: (1) Modeling damage correlation of multiple adjacent buildings in one earthquake by introducing prescribed correlation functions and generating correlated random numbers accordingly; (2) Accounting for structural non-ergodicity through Monte Carlo simulation to predict the distributions of seismic performance variables, especially in terms of cumulative damage or loss; (3) Conceptually addressing the effect of structural correlation on the loss estimation of multiple buildings in multiple events.