“…The constitutive models presented above are implemented into ABAQUS finite element software as user-defined material subroutines. The integration of soil models can be conducted by using explicit and implicit schemes, and each of them has its characteristics (Sloan, 1987, Abbo, 1997, Yang et al, 2011, Rezania et al, 2014. For the yield vertex TL model and principal stress RL model, the explicit scheme has been employed throughout to integrate them by the authors, and it proves to be an effective integration scheme (Yang and Yu, 2006, Yang and Yu, 2010, Yang et al, 2011, Yang and Yu, 2013.…”