Shaking conditions required for flame structure formation in a water-immersed granular medium

Flame structures found in sedimentary rocks may have formed from liquefaction and gravitational instability when the sediments were still unconsolidated and were subject to shaking caused by earthquakes. However, the details of the process that leads to the formation of the flame structure, and the conditions required for the instability to initiate and grow remain unclear. Here, we conduct a series of small-scale laboratory experiments by vertically shaking a case containing a water-immersed layered granular medium. The upper granular layer consists of finer particles and forms a permeability barrier against the interstitial water which percolates upwards. We shake the case sinusoidally at different combinations of acceleration and frequency. We find that there is a critical acceleration above which the instability develops at the two-layer interface. This is because the upward percolating water temporarily accumulates beneath the permeability barrier. For larger acceleration, the instability grows faster and the plumes grow to form a flame structure, which however do not completely penetrate through the upper layer. We classify the experimental results according to the final amplitude of the instability and construct a regime diagram in the parameter space of acceleration and frequency. We find that above a critical acceleration, the instability grows and its amplitude increases. Moreover, we find that the critical acceleration is frequency dependent and is smallest at approximately 100 Hz. The frequency dependence of the critical acceleration can be interpreted from the combined conditions of energy and jerk (i.e., the time derivative of acceleration) of shaking, exceeding their respective critical values. These results suggest that flame structures observed in sedimentary rocks may be used to constrain the shaking conditions of past earthquakes.