Recent research has shown that an Arbitrary Lagrangian Eulerian (ALE) formulation can be leveraged to improve the efficiency of simulating structures subjected to moving loads, such as pavements. However, when modeling pavements, subsoil characteristics are not given much importance recently, and the subsoil is often modeled by simple linear elasticity. In this work, a hypoplastic material model capable of accurately describing the behavior of cohesionless soils, is used to model the subsoil response. Additionally, the calibration of the hypoplastic model to obtain material parameters is described. Further, the logarithmic strain approach to extend this model to finite deformations is detailed, and the incorporation of this material model into a dynamic ALE formulation is explained. Finally, the results of a transient simulation of the pavement response, when subjected to a moving load, are provided.