Innovative method to simulate design earthquake motions by controllingearthquake motion phase and proposal of new performancedesign criterion

地震运动的幅值和相位特征为评价设计结构的抗震能力提供了关键信息。在这项研究中，我们提出了一种基于群延迟时间（地震运动相位对圆频率的一阶导数）和小波分析的地震运动相位特征建模的简单方法。利用已有的地震观测数据集和小波分析计算了每次地震的群延迟时间。得到了各频带群延迟时间均值和群延迟时间标准差随地震震级、多个震源参数、震源距离和当地土壤条件的回归方程。在确定群延迟时间的不确定性可以用正态分布表示之后，我们提出了群延迟时间的仿真方法。为了进一步降低该方法的复杂性，我们还提出了一种基于一阶随机微分方程的群延迟时间模拟方法。通过对采样组延迟时间相对于圆频率的积分，得到了采样相位谱。利用样相谱模拟了符合弹性设计反应谱的地震运动，并利用屈服强度需求谱研究了其特性。研究发现，屈服强度需求谱受相谱的影响较大。如果我们使用不同的样品相位谱，即使其弹性响应谱满足相同的设计弹性响应谱，也会产生不同的屈服强度需求谱。为了解决这一问题，我们提出了一种模拟独特设计地震运动的方法，该方法同时兼容给定的弹性反应谱和屈服强度需求谱。我们还开发了一种方法来模拟真实的地震运动，只使用一个相位谱的信息，考虑地震运动的因果准则。少

Both the amplitude and phase characteristics of earthquake motion provide key information needed to evaluate the aseismic capacity of designed structures. In this research we proposed a simple method for modeling the phase characteristic of earthquake motion based on group delay time (the first order derivative of an earthquake motion phase with respect to the circular frequency) and wavelet analysis. Existing data sets of observed earthquake motions and wavelet analysis are used to calculate the group delay time of each earthquake motion. Regression equations for the mean group delay time and standard deviation of group delay time in each frequency band defined in the used wavelet are obtained as functions of the earthquake's magnitude and several source parameters, hypocenter distance as well as local soil conditions. After confirming that the uncertainty of the group delay time could be expressed by the normal distribution, we developed a simulation method of group delay time. To re … More duce complexity of this method we also developed a method to simulate the group delay time based on a first order of the stochastic differential equation. A sample phase spectrum was obtained by integrating a sample group delay time with respect to the circular frequency.Using the sample phase spectrum an earthquake motion compatible with the elastic design response spectrum is then simulated, and its characteristic is investigated using the yield strength demand spectrum. Through this investigation we found that the yield strength demand spectrum was strongly affected by the phase spectrum used for an analysis. If we used a different sample phase spectrum a different yield strength demand spectrum produced even though its elastic response spectrum satisfies the same design elastic response spectrum. To solve this problem we therefore proposed a method to simulate a unique design earthquake motion, which is simultaneously compatible with both the given elastic response spectrum and the yield strength demand spectrum.We also developed a method to simulate realistic earthquake motions using only the information of a phase spectrum taking into account the causality criterion of earthquake motions. Less