Rock concerts and soccer matches: how extreme could be ground motion generated by jubilant crowds ?

There have been over last decades several examples of large ground vibrations caused by masses of people gathered for special events: a rock concert in Ullevi stadium (Gothenburg, Sweden) in 1985 generated strongly felt tribune vibrations, while there are repeated examples of seismological recordings corresponding to goals in high stake soccer matches (for instance, the famous Barca "remontada" against PSG in 2016-17 Champion's league, and the Mexico victory over Germany during World Cup 2018). Such man-induced vibrations can therefore be a concern for the design of stadium facilities, in order to avoid coincidence between structural frequencies and man-made beating frequencies (generally around 2 Hz). The present work reports a numerical investigation about how extreme could be such vibrations at ground level. We use the discrete wavenumber approach to model the wave field generated by surface sources (corresponding mainly to vertical forces) with an amplitude corresponding to the surface load estimated for jumping crowds (around 3 KPa, Erlingsson and Bodare 1999). We consider a ground layering leading to resonant frequencies close to 2 Hz, and compute the ground motion at various distances (from a few tens of meters to several kilometers). The largest ground motion is found to correspond to the center of sets of sources arranged in circles having a radius of several hundred meters, and a beating frequency tuned to the Airy phase of Rayleigh waves, and an underground structure with significant velocity contrast and low damping. In such cases, as long as the soil behaves linearly, the ground displacement is found to possibly exceed several cm, while the velocity can reach several tens of cm/s at the very center of the circle. The conditions for large vibrations are thus: efficient wave trapping in shallow soil layers (i.e., large velocity contrast), rather low damping, energetic surface waves and specific geometrical configurations (underground structure combined with source geometry). This series of results also pave the way to investigations on the use of concentric, active surface sources that could be combined to perform in-situ measurements of soil non-linear characteristics.