Rocking Response of Free-Standing Rigid Blocks on Slopes

Structure, equipment, statue or storage cask may experience free-standing rocking on slopes because of the nonuniform settlement of the base, construction error or foundation failure. The free-standing rigid block on a slope subjected to one-sine pulse excitation and earthquake motions is examined in this paper. First, considering the free-standing rigid block on a slope, the overturning acceleration spectrum under one-sine pulse is built. The spectrum covers two overturning modes, i.e. overturning with one impact either before or after the excitation and overturning without impact. Then the influences of the slope on the overturning acceleration spectrum are discussed in depth. The analytical solution is compared with the numerical solution based on both linear and nonlinear formulations. It reveals that the safe region of the minimum overturning acceleration spectrum between mode 1 and mode 2 depends on the angle of the slope. Further, the block on a slope is subjected to the Tianjin, Kobe and Northbridge earthquake motions. By simplifying the main pulse of the motions to one-sine pulse, although the overturning acceleration spectrum fails to predict the overturning acceleration of the block subjected to real earthquake motions, it can provide some guidelines to predict the practical performance of the rocking structures.