On the Resonance Conditions of Rigid Rocking Blocks

The dynamic behavior of rigid free-standing blocks subjected to earthquake ground motions is highly non-linear and sensitive to small perturbations of various parameters. Many difficulties arise in defining reliable response spectra for such systems and these are well known in the literature. This paper deals with the resonance conditions in order to highlight to what extent the ground motion details and the system parameters can influence the rocking response. The first step is the construction of an artificial input implying amplitude resonance for the motion, which is analyzed by means of a simplified equation of motion introduced by Housner (1963). The coefficient of restitution is assumed to be a variable of the problem to account also for other damping effects (e.g. local plastic deformations). A stabilized phase of the motion is identified for which an upper-bound of the maximum rotation angle of the block can be defined in closed form. The results are plotted in resonance spectra which point out the influence of the coefficient of restitution and the size and slenderness of the block. An interesting comparison with the response of an elastic damped SDOF oscillator in analogous resonance conditions is also presented. KeywordRigid block dynamics, Multiple impulses, Rocking amplification, Size effect, Resonance spectra

[1]  Yuji Ishiyama,et al.  Motions of rigid bodies and criteria for overturning by earthquake excitations , 1982 .

[2]  Ioannis N. Psycharis,et al.  Parametric investigation of the stability of classical columns under harmonic and earthquake excitations , 2000 .

[3]  G. Housner.  The behavior of inverted pendulum structures during earthquakes , 1963 .

[4]  Nicos Makris,et al.  Rocking Response of Free-Standing Blocks under Cycloidal Pulses , 2001 .

[5]  J. Penzien,et al.  Rocking response of rigid blocks to earthquakes , 1980 .

[6]  Pol D. Spanos,et al.  Rocking of Rigid Blocks Due to Harmonic Shaking , 1984 .

[7]  Harry W. Shenton,et al.  CRITERIA FOR INITIATION OF SLIDE, ROCK, AND SLIDE-RoCK RIGID-BODY MODES , 1996 .

[8]  Nicos Makris,et al.  The rocking spectrum and the limitations of practical design methodologies , 2003 .

[9]  W. K. Tso,et al.  Steady state rocking response of rigid blocks part 2: Experiment , 1989 .

[10]  W. K. Tso,et al.  Steady state rocking response of rigid blocks part 1: Analysis , 1989 .

[11]  C. Casapulla.  Lower and upper bounds in closed form for out-of-plane strength of masonry structures with frictional resistances , 2008 .

[12]  M. J. N. Priestley,et al.  SEISMIC RESPONSE OF STRUCTURES FREE TO ROCK ON THEIR FOUNDATIONS , 1978 .

[13]  Matthew J. DeJong.  Amplification of Rocking Due to Horizontal Ground Motion , 2012 .

[14]  Mohammad Aslam,et al.  Earthquake Rocking Response of Rigid Bodies , 1980 .

[15]  Tomoyo Taniguchi,et al.  Non‐linear response analyses of rectangular rigid bodies subjected to horizontal and vertical ground motion , 2002 .

[16]  Sergio Lagomarsino,et al.  Seismic assessment of rocking masonry structures , 2014, Bulletin of Earthquake Engineering.