3D Discrete Element Model and Continuum Theory for Quasi-static Granular Flow of Ice Mélange

Ice mélange is a granular pack of sea ice and icebergs that is tightly packed in tidewater glacier fjords and can suppress iceberg calving by providing resisting stresses called buttressing. Without measurements of buttressing forces provided by ice mélange, it remains challenging to predict glacial calving events and thus the mass loss of ice sheets.

To quantify the buttressing force on the glacier terminus, previous work has developed 2D discrete element models (DEM) for ice mélange. However, recent observations and experiments suggest that the mélange thickness affects its buttressing force. Here we develop a 3D DEM that simulates a moving terminus pushing against a collection of cubic icebergs that is confined within a channel. To study the effect of fjord friction on mélange behaviors, we adopt straight and rugged channel configurations. In a straight channel, the mélange moves like a plug flow with a constant buttressing force. In a rugged channel, the mélange forms shear bands and undergoes stick-slip cycles, which is evidenced by slight fluctuations in buttressing force during the steady state. We developed a 3D continuum theory to describe ice mélange in the quasi-static regime. The resulting analytical model reveals that the buttressing force depends on the square of the mélange thickness, exhibiting an excellent agreement with DEM simulations. Validated by remote observations, we conclude that the mélange thickness at the terminus must be larger than 145 meters to provide effective buttressing.