Seismic fault model for calculating exactly the dynamic motion in the stick phase and generation of short-period seismic motion

本课题提出了一种现有方法无法模拟的断面上停止阶段的运动数值计算方法。将该方法应用于摩擦实验中观测到的运动的模拟。首先，对断层面上滑动和停止阶段动态运动的分析方法进行了综述，澄清了分析断层面动态摩擦行为的数值问题：1。在停止阶段和滑动阶段，故障面上节点的自由度数不同，2。人造的短周期地震运动是由于估计滑动停止的时间不准确而产生的。3.双向滑动时动态运动的数值精度比单向滑动时差。其次，为了解决问题1。人们想出了一个新奇的主意。其思想是，在粘滞阶段接触的两个物体的运动与在滑移阶段以滑移速度为零的两个物体的运动相同。从这一思想出发，导出了杆与滑动相的相同运动方程。为了解决问题2。给出了滑移停止时滑移速度和加速度同时为零的定义。将该定义应用于Newmark积分法，提出了一种无需迭代计算滑移停止精确时间的数值方法。最后，通过对基础隔震建筑滑动轴承的滑动模拟实验，验证了所提数值方法的准确性。由于没有地震断层滑动（包括停止阶段的运动）的实验数据，因此对该实验数据进行了调整。

This research project proposed a numerical method for calculating the enact motions in the stopping phase on fault planes that the hitherto developed methods are incapable of simulating. The method was applied to the simulation of the observed motions obtained by a frictional experiment.First, the review of the analytical methods for the dynamic motions in the slippage and stopping phases on fault planes was performed The review clarified the numerical problems in analyzing the dynamic frictional behavior of fault planes : 1.the number of degree of freedom of the nodes on a fault plane is different between the stopping phase and sliding phase, 2.artificial short-period seismic motions are produced by the inaccuracy of the estimated time when a sliding will stop. 3.the numerical accuracy of dynamic motions in bi-directional sliding is worse than that in one-directional sliding. Secondly, in order to solve problem 1.a novel idea was found out. The idea is that the motions of the two body contacted in the stick phase are the same as those of the two body in the sliding phase which are slipping at the slip velocity of zero. From the idea, the identical equation of motion for the stick and the sliding phases were derived. For solving the problem 2.the definition was introduced that the slippage velocity and acceleration reach to zero simultaneously when the slippage ceases. By applying the definition to the Newmark's integration method, a numerical method to calculate the exact time when the slippage ceases without iteration was proposed. Finally, the accuracy of the proposed numerical methods were validated by simulating a sliding experiment that had been performed for sliding bearings for base isolated buildings. This experimental data were adapted since there was no experimental data seismic fault slippage including the motions in the stoppingphase.