Abstract: The existing Masing-type nonlinear soil constitutive models encounter the problem of relatively complex loading-unloading rules (eg, the "extended Masing" rule) to describe the soil stress-strain hysteresis curve under the irregular cyclic loadings such as earthquakes. It will lead to a large number of state variables during the solution, which is inconvenient to be implemented. At the same time, the existing (improved) models primarily match the shear modulus reduction curves with the damping ratio curves rarely being matched. In this paper, to overcome the above problems, a new irregular loading-unloading rule is proposed based on modified damping. The rule overcomes the "upper boundary rules", and only the current reversal point and historical maximum (minimum) point need to be stored, which greatly reduces memory. Meanwhile, it accounts for the effect of soil shear modulus and the damping ratio curve simultaneously to modify damping ratio. Then, a new nonlinear constitutive model is proposed and implemented into the Abaqus software based on the Matasovic back-bone curve and the proposed loading-unloading rule. The correctness of the proposed loading-unloading rule is verified by comparing numerical results of the site seismic response of Mississippi Bay with the results calculated by the Deepsoil software where the Davidenkov Chen Zhao (DCZ) model is adopted. To further validate the practical applicability of the proposed model, the seismic response analysis of KSRH10 site of Japan KiK-net is conducted and compared with the record of acceleration time history and spectral acceleration.

Key words: modified damping, irregular loading-unloading rule, Matasovic back-bone curve, soil nonlinearity, Abaqus software, site seismic response