Calculation of extreme accelerations in earthquake motion due to ground spalling

The occurrence of record-breaking extreme vertical acceleration, caused by the separation of the loosely attached ground and its subsequent landing, was discovered during the 2008 M w 6.9 Iwate-Miyagi earthquake in Japan. The phenomenon was termed the trampoline effect and later referred to as spalling. The trampoline model is quantitatively inaccurate, as it assumes a soft elastic rebound, whereas large accelerations could only be produced by hard collision. We present a computational model of spalling based on Hertz’s theory of solid impact and the projectile equation. It quantitatively reproduces the asymmetric shape of the acceleration time history, in which the negative phase is capped at one negative gravity, and the observed high values in the positive slapdown phase. The model predicts that the ground spalling can increase the maximum possible acceleration that can be experienced in an earthquake to seven gravities. Such a scenario should be taken into account in seismic-hazard analyses.