Abstract: This study aims to study the deformation laws of soil under cyclic loading. Based on the existing fractional dashpot, a new fractional-order Nakahara Model (FNM) was established to replace the constant dashpot in the viscoplastic body of Nishihara model under cyclic loading. This model can be used to describe various types of deformation law of soil under cyclic loading. When the stress amplitude of cyclic loading is larger than the critical stress amplitude of soil, the model is regarded as a FNM which can reflect the deformation law of soil failure. On the contrary, it is considered as a generalized Kelvin model which can reflect the law of soil stability and critical deformation. In this study, the cyclic loading was firstly decomposed into a static load and a cyclic load with zero average stress by using the stress decomposition method. Based on the established FNM, a rheology constitutive equation of soil was put forward under the static load, according to the theory of rheological mechanics. Meanwhile, a dynamic constitutive equation of soil was deduced under the alternating stress, by considering the theory of viscoelastic mechanics. Finally, a new constitutive equation of the model was obtained by superimposing the constitutive equations of soil under two different stress conditions. Compared with existing experimental results of soil, the obtained constitutive equation of soil can well describe various types of deformation law of soil under cyclic loading. Moreover, the fitting results of various types of deformation curve of soil showed good performance and the fitted correlation coefficients were above 0.90. Meanwhile, the values of model parameters decreased in power function law with the increase of the dynamic stress amplitude of cyclic loading.

Key words: soil mechanics, cyclic loading, fractional-order dashpot, generalized Kelvin model, fractional-order Nakahara model, deformation characteristics