AUTHOR=Homma Sae , Nabeshima Kunihiko , Takewaki Izuru 

TITLE=Explicit Overturning Limit of Rigid Block Using Triple and Pseudo-Triple Impulses Under Critical Near-Fault Ground Motions

JOURNAL=Frontiers in Built Environment

VOLUME=Volume 7 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/built-environment/articles/10.3389/fbuil.2021.731670

DOI=10.3389/fbuil.2021.731670

ISSN=2297-3362

ABSTRACT=An explicit limit for the overturning of a rigid block is derived on the input level of the pseudo-triple impulse as a modified version of the triple impulse that is 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 (kinematic and potential).  The initial velocity of rotation after the first impulse and the velocity change of rotation 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 velocity change 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 prevents the computation of complicated non-linear time-history responses.  The critical timing of the second impulse (also the third impulse timing to the second impulse) is characterized 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 derived from the explicit expression of the critical velocity amplitude limit of the pseudo-triple impulse that its limit is proportional to the square root of size, i.e. the scale effect.  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.