Estimating a Crack Growth Parameter for the Sulzberger Ice Shelf from Tsunami-Induced Calving

The vibration response of a cracked ice shelf to tsunami wave forcing is studied. In particular, the tsunami-induced calving events in the Sulzberger Ice Shelf in 2011 and 2022 are investigated. It is shown that the wave amplitudes and frequencies were similar for both events at the locations near the ice shelf location. A simple thin plate model in shallow water with a rotational spring condition is used to model the crack. The time-domain response is reconstructed from the wave-frequency response for incident wave packets with similar frequencies and amplitudes to the measured tsunami waves, and the stress field is calculated to evaluate the crack-tip stress intensity. Motivated by the cyclic nature of the loading, Paris’ law for crack growth is investigated as a plausible phenomenological model for progressive crack growth. The Paris’ law parameters are treated as effective model parameters because fatigue parameters for large-scale Antarctic ice shelves are not experimentally constrained. A multi-parameter sensitivity analysis quantifies the dependence of crack-growth rates and predicted failure cycles on the Paris exponent, initial crack depth, crack-depth ratio, shelf thickness, and assumed failure duration. This work is presented as a preliminary study demonstrating how these rare geophysical phenomena can be used to constrain effective crack-growth parameters and investigate their sensitivity.