Assessment of the effectiveness of Multiple-Stripe Analysis by using a stochastic earthquake input model

Abstract

Current practical approaches for probabilistic seismic performance assessment of structures rely on the concept of intensity measure (IM), which is used to decompose the problem into hazard analysis and conditional seismic demand analysis. These approaches are potentially more efficient than traditional Monte-Carlo based ones, but the performance estimates can be negatively influenced by inadequate setup choices. These include, among the others, the number of seismic intensity levels to consider, the number of structural analyses to be performed at each intensity level, and the lognormality assumption for the conditional demand. This paper investigates the accuracy and effectiveness of a widespread IM-based method for seismic performance assessment, multi-stripe analysis (MSA), through an extensive parametric study carried out on a three-story steel moment-resisting frame, by considering different setup choices and various engineering demand parameters. A stochastic ground motion model is employed to describe the seismic hazard and the spectral acceleration is used as intensity measure. The results of the convolution between the seismic hazard and the conditional probability of exceedance obtained via MSA are compared with the estimates obtained via Subset Simulation, providing a reference solution. The comparison gives useful insights on the influence of the main parameters controlling the accuracy and precision of the IM-based method. It is shown that, with the proper settings, MSA can provide risk estimates as accurate as those obtained via Subset Simulation, at a fraction of the computational cost.

Appendix

The present Appendix provides some details about the construction of the IM hazard curves ν_IM (im) via Subset Simulation (Au and Beck 2003). For this aim, Subset Simulation is performed by considering l = 20 levels, each having a target intermediate exceedance probability p₀ = 0.5 and n_sim = 500 analyses per level. Consequently, 500 ground motion samples are generated, from a stochastic ground motion model, within each of the l simulation levels, which also correspond to the intervals of discretization of the IM hazard curve obtained in output. Indeed, the hazard curve discretisation follows from the IM intermediate thresholds generated during the Subset Simulation run.

To be precise, Subset Simulation provides IM hazard curves with inferior limit corresponding to the annual rate of exceedance $\bar{\nu }$ = 0.316 1/year, identifying the rate of occurrence of earthquakes of any magnitude between m₀ and m_max; the superior limit, $\hat{\nu }$ = 3·10⁻⁷ 1/year, corresponds to $\bar{\nu } \cdot p_{0}^{l}$. In conclusion, by including the lower bound $\bar{\nu }$, v_IM is discretized in a total of 21 points, corresponding to n_IM = 21 IM levels or stripes.

Among the 500 ground motion samples generated at each IM level, a subset of n_sim = 20 samples is selected to represent the record-to-record variability effects conditional on the IM level.