“…The subgrade is regarded as the support layer for the pavement or railway structures and undertakes the dynamic stress induced by the moving traffic loadings (Beskou and Theodorakopoulos, 2011;Krechowiecki-Shaw et al, 2016;Bian et al, 2018;Cui et al, 2022;Cui et al, 2023a;Cui et al, 2023b;Cui et al, 2024). Under long-term cyclic loadings, the accumulative plastic deformation of subgrade soils gradually increases, where the accumulative plastic deformation induced by long-term traffic loading accounts for the majority (75%-90%) of the total permanent deformation of the subgrade (Li and Selig, 1996;Chai and Miura, 2002;Puppala et al, 2009;Cui et al, 2014;Cai et al, 2018;Lu et al, 2018;Zhang et al, 2020a;Zhao et al, 2024).…”