Changes in grain size during the stress relaxation stage of viscoelastic firn

Abstract

ABSTRACT Changes in grain size of two firn (density from ∼550 to ∼820–840 kg m−3) samples, extracted at Summit Greenland during their stress relaxation over 3 days were observed using optical micrographs. These changes were confirmed by both 3-D microstructural reconstruction images and plots of microstructural parameters vs. time, viz., the grain size increased with the decrease of pore size, the specific surface area, and the index of prevalent ice curvature. Building on studies of both the viscoelastic behaviour of firn deformation and the measured changes in grain size, a quadratic-based model is constructed to describe the evolution of grain size during the stress relaxation stage, where the grain growth is in relation to the microstructure, the relaxation time, and the threshold stress (an equilibrium residual stress at the grain size maximum, which forces the grain growth before the arrival of the grain size maximum). This model can be scaled up from laboratory samples to the glaciers and ice sheets, e.g. the time at the grain size maximum spanning across days to thousands of days, even to a geological age. In addition to the firn samples which have undergone the stress relaxation prior to laboratory tests, especially sensitive to the effect of grain size, should be calibrated, this work also sheds light on learning more about the mechanical behaviours and changes in grain size during the deformation of firn or other porous materials under interrupted or cycle load, particularly from the stress relaxation, irrespective of the compression, tension, or shear.