Pressure response on granular impacts: how far the Boussinesq model can go?

The Boussinesq law is one of the classical models to predict the overpressure inside a soil induced by applying a single static load. In the present report, we question how this model can be extended when dealing with granular impacts. For this, we have conducted experimental measures of the pressure distribution at the bottom of a quasi-uniform dry sandy deposit impacted by a steel sphere of 8cm diameter, falling from dropping heights variable up to 100 cm. Our measures shown that this distribution follows a symmetrical Boussinesq-like form, characterized by a center peak of pressure that can be modeled by assuming a simple point-force model acting at the granular pile's surface. This point-force considers the contribution of the weight of the intruder and its momentum at the impact time. To the best of our knowledge, this is the first time where these kinds of measures are reported for granular beds, proposing at the same time many questions and challenges deserving to be explored with more detail.