Permanent, inelastic deformations of one or several pavement and subgrade layers originate from insufficient material (mix rutting) or structural design (subgrade rutting) of the asphalt pavement setting subjected to periodic traffic load (frequency- and load-dependent). Several studies revealed that the correct numerical assessment of the complex tire-pavement interaction (detailed consideration of tire and pavement) is crucial for reliable and accurate long-term predictions. In this contribution, the structural long-term response of asphalt pavements (modeled as elastoplastic solid at large strains) under periodic traffic load is thermo-mechanically investigated within the finite element method (FEM). To efficiently predict irreversible, permanent deformations of the pavement surface due to repetitive tire overrun, the time homogenization technique in combination with an Arbitrary Lagrangian Eulerian (ALE) formulation for the finite element (FE) discretized tire and pavement structures is employed. Time homogenization is used to deal with different time scales in the response of the tire-pavement system to short-term loading (tire overrun), day-night as well as seasonal temperature changes over several years. Different aspects and influence quantities for the problem considered are discussed and enable a qualitative prediction of pavement rutting via a fully FE based approach for tire and pavement instead of traditionally used mechanistic-empirical (M-E) approaches.