A new indentation model for snow

Plate indentation tests have been used widely to characterize the properties of terrains. In particular, pressure–sinkage curves obtained from these tests have been used for vehicle–terrain interaction predictions. However, there is a lack of physical basis to properly interpret the meaning of these empirical curves such that they cannot be related to fundamental material properties. Also, the relation between the plate indentation tests and static (non-rolling) pneumatic tire indentation is not clear. In this paper, we conducted finite element analysis of circular plate indentation and static tire indentation simulations for fresh snow of different depths. The results indicate that the pressure–sinkage relationship for the plate indentation test is qualitatively similar to that for static tire indentation. Three deformation zones have been identified for these tests using pressure–sinkage and density–sinkage data: a small elastic zone (Zone I), a propagating hardening plastic zone (Zone II) and a densification (finite depth) zone (Zone III). The onset of a finite-depth zone was identified where the pressure bulb beneath the plate/tire has reached the bottom of snow. It is shown that Zone I and Zone II correspond to a semi-infinite terrain typical of vehicle–soil interaction, whereas Zone III corresponds to a finite-depth domain for snow and other multilayered media. The plastic constraint underneath the indenters suggests a quasi-uniaxial stress state such that a simple 1-D indentation model was proposed for Zone I, a spherical cavity expansion solution was adapted for Zone II, and an upper bound solution was adapted for Zone III. The results of the prediction of the transition between Zone II and Zone III as well as the pressure–sinkage relationships compared well with finite element solutions of plate indentation and static tire indentation tests, and with field data.