Validation of modified irregular loading-unloading rules based on Davidenkov skeleton curve and its equivalent shear strain algorithm implemented in ABAQUS

Under irregular cyclic loadings, adopting the extended Masing criterion to modify the stress-strain hysteresis curves will bring about the program with a large number of state variables. In this paper, the initial stress-strain skeleton curve is simulated by the Davidenkov model, and the simplified loading-reloading rules are proposed instead of the upper boundary rules of the extended Masing criterion. Through comparison, an equivalent strain algorithm with simple unloading judgment standard and higher precision is proposed. Synthesizing computational accuracy and efficiency of large-scale nonlinear seismic site effect analyses, a three-dimensional explicit subroutine of the Davidenkov model with simplified loading-reloading rules is developed in ABAQUS/Explicit module. It is applicable to both two- and three-dimensional seismic site effect analyses. Finally, a two-dimensional numerical simulation for a soil column 500 m thick of Mississippi Embayment is carried out, the peak ground accelerations versus different seismic levels, site seismic responses for Kobe earthquake record of PGA 0.65g are compared with those computed by one-dimensional nonlinear seismic site response analysis program Deepsoil. The results show that the modified irregular loading-unloading rules based on the Davidenkov skeleton curve and the proposed equivalent strain algorithm are rational and valid.