Simulation of Tire-Snow Interfacial Forces for a Range of Snow Densities with Uncertainty

The objective of this paper is to assess the effect of snow density on tire-snow interaction in the presence of uncertainty. The snow-depth dependent finite element analysis (FEA) and semi-analytical models we have developed recently can predict tire-snow interfacial forces at a given density under combined slip conditions. One drawback of the models is that they are only applicable for fresh, low-density snow due to the unavailability of a density-dependent snow model. In reality, the snow density on the ground can vary between that of fresh snow to heavily compacted snow that is similar to ice. Even for fresh snow on the ground, as a vehicle moves forward, the rear wheels experience higher snow densities than the front wheels. In addition, being a natural material, snow's physical properties vary significantly even for the same density. The purpose of this paper is then to develop a preliminary density-dependent engineering snow model for a wide range of densities and to apply the model to tire-snow interaction taking into consideration the uncertainty of snow properties. Snow is considered as a pressure-sensitive Drucker-Prager material where the Drucker-Prager yield criterion is employed to establish the relationship between strengths in compression/tension and other material parameters. The uncertainties of snow properties are characterized using the principles of interval analysis. The bounds of Drucker-Prager parameters against density are analytically derived. The bounds of snow sinkage, motion resistances and shear forces, at different densities under combined slip conditions, are achieved through constrained optimization.