Publication

Abstract : This paper describes an analytical and numerical study performed to benchmark LS-DYNA computer analysis of the response of a stacked spent fuel cask system to seismic base excitation. The LS-DYNA solution of the rocking block problem and stability of the block under the action of a base acceleration pulse are compared to the inverted pendulum solution first published by George W. Housner in 1963. Housner’s work has been cited by a number of subsequent investigations exploring the physics behind the rocking block problem, including Yim and Chopra [2]. The analytical formulation of the rocking block problem is derived in 2D in this paper. As is the case in many of the previous formulations, the solutions are provided after linearization of the governing equations. The stability of the unanchored block subjected to an acceleration pulse is solved using the energy method. The solution displays key differences relative to Housner’s minimum acceleration required to overturn. An alternate equation for effective viscous damping is also presented, which differs from the formulation given in Appendix A of ASCE 43-05 [9]. Simulation of the rocking block problem using LS-DYNA is shown to faithfully reproduce the classical solution, albeit at lower levels of energy loss. Effective damping and minimum acceleration to overturn from the LS-DYNA benchmark agree with predictions of the classical solution even after linearization.