“…For the subgrade materials, many researchers proposed different standards to judge the permanent deformation behaviors and calculated the different deformation areas boundaries and critical dynamic stress, such as for unbound granular material (Gu et al, 2017;Xiao et al, 2018a;Xiao et al, 2018b;Zhao et al, 2022), coarse-grained soil (Leng et al, 2017;Zhai et al, 2020;Wang and Zhuang, 2021), fine-grained soil (Zhang et al, 2020b;Li et al, 2021;Cui et al, 2023c), and frozen soil (Wang et al, 2018;Zhou et al, 2020;Zhou et al, 2022). For the highway engineering practice, the sustainable design and hazard prevention of pavement structures demand an in-depth understanding of the plastic deformation and shakedown behavior of the thawed subgrade soils to further meet the requirement of long-term serviceability.…”