Numbers of records and input directions required for structural deterministic and probabilistic performance assessments
摘要
Accurate estimation of the seismic demand of buildings requires carefully considering both the ground motion group size (n) and the angle of seismic input (ASI). Existing studies focus more on the relative effect of either n or ASI on evaluation results. There is ongoing debate on the n and ASIs required in deterministic and probabilistic seismic performance assessments, and no specific guidelines have been established for engineering practice. To address this concern, this study proposes a framework for assessing statistical bias of response and providing engineering-oriented recommendations for n and ASI in nonlinear response history analysis of mid-rise buildings. Firstly, a regrouping procedure is presented to generate 100 suites of ground motions with a specified smaller size of n from a benchmark large dataset of ground motions. Next, three statistical indices are defined to precisely characterize the bias between the small-sample and benchmark large-sample ground motions, namely bias(µ), sdev(µ), and bias(β), which quantifies the effects of n and ASI on errors of the estimated central tendency and variability of response in deterministic and probabilistic analyses. Based on an acceptable statistical bias, the required values of n and ASI for different conditions are recommended. Finally, to facilitate practical application, a simple yet efficient model of the correction coefficient (κ) of variability is proposed to save computational time and improve assessment accuracy. Results show that at least 10 pairs of records and 4 input directions are required to ensure reliable estimates of expected seismic response for mid-rise buildings. The bias in variability can be adjusted using the κ. These engineering-practical recommendations contribute to resolving the ongoing debate regarding the necessary n and ASI in seismic performance assessments of mid-rise buildings.