Scale Effects in Strength-Dominated Collisions of Rocky Asteroids

The application of laboratory collision experimental results to the larger scales of asteroid impacts is complicated by the fact that the dynamic strength of rock typically decreases as the loading duration increases. Because loading times increase with the size scale of a collision, large bodies are effectively weaker than small ones. While this effect has been postulated for over a decade, it has never been verified in actual collision experiments. This paper summarizes collision tests performed under the conditions required to examine scale effects, i.e., increasing the size scale of the experiment while holding the impact velocity and impact kinetic energy per target mass constant. Granite targets are used, with a diameter variation of a factor of 18. The larger targets experienced significantly more collisional damage than small ones, confirming a decrease in dynamic strength with increasing size scale. The results are compared to a scaling model based on the concept that fragmentation is accomplished through the growth and coalescence of preexisting flaws. Measurements of the actual flaw-size distribution are used to validate the model. Field observations of flaw and fault sizes at scales to 10~km are used to construct a scaling model that is believed to apply to the shattering of a wide range of rock types. The results show that kilometer-sized rocky bodies may be significantly weaker than indicated by previous estimates.