Development of a mathematical model describing the interaction of compacted snow mass with pneumatic tires

To develop a mathematical model describing the interaction of a pneumatic wheel with a snow mass during the construction of winter roads, the Bingham—Shvedov mathematical model based on the Maxwell—Thompson viscoelastic rheological model was defined as the model of plastic deformations. Based on the analysis, a combined model of snow cover was compiled to take into account the elasticity, viscosity and plasticity of the snow cover, with the replacement of the viscous element in the Kelvin—Voigt model by the Bingham—Shvedov viscoelastic model and sequentially connected with the additional Bingham model, since the Bingham—Shvedov element allows one to take into account the loss of the bearing capacity of the snow cover. The proposed model introduces the division of plastic deformation into two components developing at different rates. Keywords mathematical model, snow mass, tire, compaction, elastic-viscoplastic properties, pneumatic-tire roller, wheel deformation