Explicit Overturning Limit of Rigid Block Using Triple and Pseudo-Triple Impulses Under Critical Near-Fault Ground Motions
Explicit Overturning Limit of Rigid Block Using Triple and Pseudo-Triple Impulses Under Critical Near-Fault Ground Motions
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DOI：
10.3389/fbuil.2021.731670
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
Sae Homma;K. Nabeshima;I. Takewaki
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文献类型：
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作者：
Sae Homma;K. Nabeshima;I. Takewaki
以三重冲量和拟三重冲量的输入水平为基础，推导了刚性块体倾覆的显式极限，作为三重冲量的修正形式，替代了近断层正向方向性地面运动。应用角动量守恒定律和机械能守恒定律(动能守恒定律和势能守恒定律)描述了刚性块的倾覆行为。利用角动量守恒定律确定了第一冲量后的初始转速和由于转动中心的移动而撞击地面后的转速变化。根据机械能守恒定律，求出了第一冲量后的最大转角。二次冲量后的转速变化也符合角动量守恒定律。根据机械能守恒定律，还推导了刚性块在二次冲击后的最大转角，这是计算倾覆极限所必需的。这使我们可以避免计算复杂的非线性时程响应。第二冲量的临界时序(也就是第三冲量到第二冲量的时序)是指第一冲量之后的撞击时间。与双脉冲的情况一样，紧接在撞击之后的第二个脉冲的动作被用作关键时序。从伪三冲量临界速度幅值的显式表达式出发，得出其极限值略大于双冲量的极限值。最后发现，当考虑三重冲量中的第三个冲量时，刚性块倾覆的极限输入速度大于伪三重冲量的极限输入速度。这是因为第三个冲量被认为是通过向刚性块的振动的相反方向施加冲击来防止刚性块倾覆。
An explicit limit for the overturning of a rigid block is derived on the input level of the triple impulse and the pseudo-triple impulse as a modified version of the triple impulse that are a substitute of a near-fault forward-directivity ground motion. The overturning behavior of the rigid block is described by applying the conservation law of angular momentum and the conservation law of mechanical energy (kinetic and potential). The initial velocity of rotation after the first impulse and the change of rotational velocity after the impact on the floor due to the movement of the rotational center are determined by using the conservation law of angular momentum. The maximum angle of rotation after the first impulse is obtained by the conservation law of mechanical energy. The change of rotational velocity after the second impulse is also characterized by the conservation law of angular momentum. The maximum angle of rotation of the rigid block after the second impulse, which is mandatory for the computation of the overturning limit, is also derived by the conservation law of mechanical energy. This allows us to prevent from computing complex non-linear time-history responses. The critical timing of the second impulse (also the third impulse timing to the second impulse) is featured by the time of impact after the first impulse. As in the case of the double impulse, the action of the second impulse just after the impact is employed as the critical timing. It is induced from the explicit expression of the critical velocity amplitude limit of the pseudo-triple impulse that its limit is slightly larger than the limit for the double impulse. Finally, it is found that, when the third impulse in the triple impulse is taken into account, the limit input velocity for the overturning of the rigid block becomes larger than that for the pseudo-triple impulse. This is because the third impulse is thought to prevent the overturning of the rigid block by giving an impact toward the inverse direction of the vibration of the rigid block.