The rocking and overturning of a variety of structures, such as electrical equipment, retaining walls, liquid storage tanks, tall rigid buildings and tombstones, and the need for understanding and predicting these failures in association with the attempt of estimating the related intensity levels of ground motion have motivated a number of studies on the rocking response of rigid blocks [1,2,3,4,5].

Actually when a rigid block is rocking, it is assumed that the rotation continues smoothly from one base edge to the other, without any sliding, vertical displacement component or rotation around the vertical axis. This rotational constraint, in association with conservation of momentum, requires an energy loss during impact that emerges from the requirement that the block sustains rocking motion [4].

The energy loss during impact depends on the slenderness of the block. An energy loss during impact, that is greater than the minimum energy loss required for the realization of rocking motion, results in a more rapid decay of the vibrations [6]. Up to now a number of papers is available in literature, aimed at demonstrating this feature, which was justified experimentally [7,8,9].

In this research he pure rocking of the blocks from an experimental point of view by means of a shaking table is studied; experiments are developed on rectangular aluminum blocks of various sizes and geometry ratios.

For developing experiments, a unidirectional shaking table is used at the Laboratory of "Scienza delle Costruzioni" of the University of Naples "Federico II", and dynamic tests on rigid blocks are executed; in order to obtain experimental data on blocks' rocking, the blocks are suitably fixed on the moving table and an accelerometer is placed on the top of each block, measuring its accelerations.

Experiments are set up in such a way to have the impact or pivotal points between the block and the base plane at well defined positions, which results in the two requirements that no sliding of the model should occur on the base and that the blocks are sufficiently stiff such as to be considered rigid; one thus has only rotations around the two base edges of the blocks, according to the motion of the shaking table.

After obtaining laboratory data from experimental investigation, one observes that the rocking response of the blocks is very sensitive to small changes in their size and slenderness ratio and to the details of the ground acceleration.

Generally speaking, peak accelerations appear to be higher on stockier blocks, and apparently more stable blocks, showing an unexpected effect which makes the larger of two geometrically similar blocks less stable than the smaller one.

It is also noticed that the stability of a slender block subjected to a sine-wave base acceleration is much greater than the one that should be inferred from its stability against a constant horizontal force. In the light of these facts, the occasional survival of a slender structure that is apparently highly unstable is not surprising.

1

S.J. Hogan, "The many steady state responses of a rigid block under harmonic forcing", Int. J. Earthquake Eng. & Struct. Dyn. 19, pp. 1057-1071, 1990. doi:10.1002/eqe.4290190709

2

J. Milne, "Experiments in observational seismology", Trans. Seism. Soc. Japan 8, 12-64, 1881.

3

J. Perry, "Note on the rocking of a column", Trans. Seism. Soc. Japan 3, pp. 103-106, 1881.

4

G.W. Housner, "The behaviour of inverted pendulum structures during Earthquakes", Bull. Seism. Soc. Am., 53(2), pp. 404-417, 1963.

5

J. Zhang, N. Makris, "Rocking Response of Free-Standing Blocks Under Cycloidal Pulses", Journal of Engineering Mechanics 127(5)L 47383, ASCE, 2001. doi:10.1061/(ASCE)0733-9399(2001)127:5(473)

6

C.S. Yim, A.K. Chopra, J. Penzien, "Rocking response of rigid blocks to earthquakes", Earthquake Engrg. Struct. Dyn., 8(6), pp. 565-587, 1980. doi:10.1002/eqe.4290080606

7

M. Aslam, W.G. Godden, D.T. Scalise, "Earthquake rocking response of rigid bodies", J. Engrg. Mech. Div. ASCE 106(2), pp. 377-392, 1980.

8

W.K. Tso, C.M. Wong, "Steady state rocking response of rigid blocks. Part 2: Experiment", Int. J. Earthquake Eng. & Struct. Dyn. 18, pp. 107-120, 1989. doi:10.1002/eqe.4290180110

9

A. Anooshehpoor, T.H. Heaton, B. Shi, J.N. Brune, "Estimates of the ground acceleration at Point Reyes station during the 1906 San Francisco earthquake", Bull. Seism. Soc. Am., 89(4), pp. 843-853, 1999.

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