The rocking movement of a rectangular rigid block (6x30 cm) is numerically simulated. The movement starts at an inclination close to the indifferent equilibrium with a zero initial velocity. Friction is high enough to avoid any sliding of the block [Movie 1].
Numerica simulation of the movement of a rigid block subjected to a single sine-pulse ground motion. The block has a height of 3.113 m and a width of 0.795 m, the coefficient of restitution is 0.9. The sine-pulse has a period of 0.5872 s and amplitudes of 15.50 m/s2 [Movie 2], 15.52 m/s2 [Movie 3], and 17.6 m/s2 [Movie 4]. In the first case the block experiences one impact on the base before it overturns in the direction of the first half cycle of the ground motion. The slightly larger acceleration [Movie 3] does not overturn the block. The large acceleration [Movie 4] of the third experiment overturns the block to the opposite side of the initial movement without impact on the base. Parameters in these experiments are those used by Zhang and Makris (2000).
Two test columns one monolithic (on the right side) and one consisting of 7 identical column drums (on the left side) are excited be different ground motions.Both columns have a height, h of 3.5 m and the diameter, d is varied so that the h/d-ratio is between 3.0 and 9.0. The first ground motion [GM23] was measured during the Parkfield (2004) earthquake; the second ground motion [GM20] is from the 1999 Koekali earthquake, and the last one [GM18] from the Erzinkan (1992) earthquake.
For each of the three ground motions the column movements are animated for 7 h/d-ratios. Clicking the appropriate X in the following table starts the animations. (Size of the MP4 files varies between 200 and ca. 700 KB.)
| h/d | GM23 | GM20 | GM18 |
| 3.0 | X | X | X |
| 4.0 | X | X | X |
| 5.0 | X | X | X |
| 6.0 | X | X | X |
| 7.0 | X | X | X |
| 8.0 | X | X | X |
| 9.0 | X | X | X |
The QScmp code by Wang (1999) was used to calculate surface displacements of two earthquake scenarios, which were used as input for numerical modeling of the toppling behavior of the test columns described above. The two earthquakes are modeled as point sources at 10 km depth with a seismic moment of 4x1019Nm. The first example [Fig. 1] is a strike slip event on a NS-striking and 80° dipping fault plane. The second event [Fig. 2] has a normal faulting mechanism (rake = 70°) on a 60° dipping and 30°N striking fault plane. Arrows in the time snapshots between 1 and 10 seconds indicate the horizontal ground motion amplitude and direction. Color of the arrows indicates the amplitude of the vertical component.
Movie 1 [H.264-encoded MP4 File; 338 KB] shows the numerical simulation of the free rocking movement of a rectangular marble block measuring 6x8x30 cm.
Movie 2 [H.264-encoded MP4 File; 235 KB] shows the numerical simulation of the rocking movement of a rectangular block (h=3.113 m, b= 0.795 m) subjected to a single sine-pulse of 0.59 s duration and max. acceleration of 15.50 m/s2. The block overturns in the direction of the movement of the first half cycle after one impact on the base.
Movie 3 [H.264-encoded MP4 File; 244 KB] shows the numerical simulation of the rocking movement of a rectangular block (h=3.113 m, b= 0.795 m) subjected to a single sine-pulse of 0.59 s duration and max. acceleration of 15.52 m/s2. The block does not overturn.
Movie 4 [H.264-encoded MP4 File; 212 KB] shows the numerical simulation of the rocking movement of a rectangular block (h=3.113 m, b= 0.795 m) subjected to a single sine-pulse of 0.59 s duration and max. acceleration of 17.6 m/s2. The block overturns in the opposite direction of the movement of the first half cycle without any impact on the base.
GM23 [H.264-encoded MP4 File; 621 KB] shows a perspective view of the ground displacement measured during the Parkfield (2004) earthquake, labeled GM23 in the paper. Epicentral distance and backazimuth are 8.4 km and 316.0°, respectively. The grid width is 0.5 m.
GM20 [H.264-encoded MP4 File; 1004 KB] shows a perspective view of the ground displacement measured during the Koekali (1999) earthquake labeled GM20 in the paper. Epicentral distance and backazimuth are 10.0 km and 166.9°, respectively. The grid width is 0.5 m.
GM18 [H.264-encoded MP4 File; 739 KB] shows a perspective view of the ground displacement measured during the Erzinkan (1992) earthquake labeled GM18 in the paper. Epicentral distance and backazimuth are 12.6 km and 107.4°, respectively. The grid width is 0.5 m.
Snapshots are shown of the synthetic displacement ground motion field from a strike slip [Fig. 1] and a normal faulting [Fig. 2] earthquake. Theses ground motions were input for the archaeoseismic column model at 20 locations (open circles) selected randomly in a 40x40 km area centered at the epicenter.
