目标谱选波方法在算术与对数坐标下的差异分析

Analysis of differences between spectral matching method in arithmetic and logarithmic coordinates

目前时程分析选波常采用目标谱法,即选择反应谱与目标谱有较好匹配的地震波。目前为止,关于在谱匹配中采用不同的坐标体系会给地震波缩放以及时程分析结果造成的差异性影响,还鲜有相关研究结果。本文旨在对比分析谱匹配中反应谱与目标谱采用算术值(算术坐标下ASM方法)和对数值(对数坐标下LSM方法)所得结构非线性时程分析结果的差异。以美国SAC Steel Project提出的3层、9层和20层钢框架结构为实例,以该计划提出的代表3种超越概率(即50年超越概率50%、10%和2%)的各组地震波平均反应谱作为目标谱,以这3组地震波(每组20条波)时程分析所得最大层间位移角的算术均值和几何均值作为目标反应,以简单地震信息初选的小型地震波数据库(共40条波)作为备选波,将ASM和LSM方法优选出的7条地震波所得时程分析结果进行了差异性分析。研究表明, LSM方法所得地震波的缩放系数明显大于ASM方法,并且地震波的排序即选择结果也存在一定差异。ASM和LSM方法对结构反应均值(算术均值和对数均值)估计的准确度均控制在±20%以内,但LSM方法所得结构反应更大。LSM方法在降低结构反应离散性方面较ASM方法更有优势,且对于较长周期结构(如20层结构)及结构非线性程度较高(如50年超越概率10%、2%)时,这种优势会更为凸显。

In some recent studies, spectral matching is the most commonly proposed method for selecting earthquake records in time-history analysis of structures. But until now there is no serious investigation about the effects of the coordinate values on the scaling of ground motions. This paper investigated the influence of using arithmetic and logarithmic values of response spectra in spectral matching(i.e. ASM and LSM methods) on the results of nonlinear structural time-history analysis. The 3-story, 9-story and 20-story steel moment resisting frame structures proposed for the American SAC Steel Project, which represent the low-, medium-, and high-rise buildings, were used as the examples. The target spectra were the average spectral accelerations for the three ground motion sets developed in the American SAC Steel Project representative of 50%, 10%, and 2% probabilities of being exceeded in 50 years, respectively, and every ground motion sets included 20 records from 10 stations. The arithmetic mean and median of maximum inter-story drift ratios calculated from the three ground motion sets were taken as the benchmark seismic responses. The 40 records selected based on earthquake scenarios were used as the database for the selection. The structural mean(median) responses under the optimal seven records selected with ASM and LSM methods were compared. The scale factors calculated by LSM method are larger than that of ASM method,and then the ranking results of the records selected are also different. The estimation accuracies of structural mean(median) responses by both methods can be controlled in ±20%, but the structural response results calculated by LSM method are larger than that of AMS method. LSM method has better capacity to reduce the variability of the structural response results than ASM method, and the advantage is more significant for longer-period structures(e.g. 20-story structure) with severer nonlinear response(e.g. 10% and 2% probabilities of being exceeded in 50 years).