•A novel framework was developed to implement an accurate description on TPS of rutting.•A new dimensionality reduction method was constructed to avoid the repetition of indexes.•The categorization and time-dependent evolution of TPS were conducted.•Different types of TPS correspond to different index systems. This study aims to characterize the transverse profile shapes (TPSs) of rutting on asphalt pavement and to produce useful information to the highway administration in what concerns rutting. A novel framework was developed to implement an accurate description on rutting, which integrates four steps (data acquisition, TPS adjustment, TPS categorization and indicator analysis). Various indexes were analyzed and used to characterize these profiles. A new dimensionality reduction method was constructed based on correlation coefficient matrix (CCM) to avoid the repetition of indexes. These data from the Long-Term Pavement Performance (LTPP) program were collected and screened in the study. The categorization and time-dependent evolution of TPS were conducted based on the developed framework. The statistical analysis and dimensionality reduction of these indexes were carried out. Results show that the established framework allows to categorize and accurately describe the TPS of rutting. The TPSs are divided into five typical shapes and an irregular shape, and the type 5 and the irregular shape are not very valuable. There are different time-dependent evolutions for various types of TPS, which may be associated with trajectory of vehicles. The obtained critical value of these indexes should be attracted an attention from road administrations. The constructed dimensionality reduction method is capable of eliminating the redundancy of indexes, and thus optimizing the characterization effects. Different types of TPS correspond to different index systems. Extensive work on the application of information proposed in this study is still need in predicting pavement performance and conducting maintenance decision-making in further.