Parametric study in rocking instability of a rigid block under harmonic ground pulse: A unified approach

In this work a parametric study of the (overturning) rocking instability of a free-standing rectangular rigid block under a ground harmonic pulse is thoroughly discussed assuming that the friction between the rigid block and ground surface is sufficiently large to exclude sliding. Attention is focused on the minimum amplitude ground acceleration which yields (overturning) rocking instability. The individual and coupling effects on overturning instability of the stockiness parameter of the block (width to height ratio) in connection with the height of the rigid block and its initial conditions (imperfections) are examined in detail. Two modes of rocking instability with or without impact under a one-sine and a one-cosine pulse with different ground excitation periods are discussed. With the aid of phase-plane portraits rocking instability criteria which lead to closed form solutions for establishing the minimum amplitude ground acceleration, are properly assessed.

► A parametric study of the instability of a rectangular rigid block under ground harmonic pulses is presented.
► The effects of the dimensions of the rigid block and its initial conditions are investigated.
► The higher the block, the larger the minimum amplitude acceleration becomes.
► Decreasing values of angles θο and increasing values of initial angular velocity θ̇o tend to stabilize the block.
► Positive values of θ̇o and θο have a detrimental effect on the stability of the rigid block.