“Buoyancy” in granular medium: How deep can an object sink in sand?

• Buoyancy effect in granular systems.
• Measured the sinking depth (SD) of the ball into granules of different sizes.
• SD is very sensitive to the size of granular system.
• Ratio does not depend on the density of the ball and the volume fraction of granules.
• Empirical formula of SD is obtained.

The behavior of granular matter is different from either fluids or solids. One may not be able to answer even a naive question such as how deep an object can sink in sand. Answers to the depth of footprints on sand beach and its dependence on grain size have never been seriously studied before, and may deserve a closer look and better understanding. Laying a ball of fixed size onto granules, we have measured the sinking depth (SDSD) of the ball into granules of different sizes and studied the dependence of SDSD on the sizes of the ball and granules. We find that the SDSD is very sensitive to the size of granules and the variation of SDSD on granule size is not monotonic. The maximum SDSD occurs at r≈120R, where rr and RR are the radii of granules and the ball, respectively. This ratio does not depend on the density of the ball and the volume fraction of granules. An empirical formula of SDSD on densities and sizes of the ball and granules are obtained based on the experimental results.