Constitutive models of sands play an essential role in analysing the foundation responses to cyclic loads, such as seismic, traffic and wave loads. In general, sands exhibit distinctly different mechanical behaviours under monotonic, regular and irregular cyclic loads. To describe these complex mechanical behaviours of sands, it is necessary to establish appropriate constitutive models. This study first analyses the features of hysteretic stressstrain relation of sands in some detail. It is found that there exists a largest hysteretic loop when sands are sufficiently sheared in two opposite directions, and the shear stiffness at a stress-reversal point primarily depends on the degree of stiffness degradation in the last loading or unloading process. Secondly, a stress-reversal method is proposed to effectively reproduce these features. This method provides a new formulation of the hysteretic stress-strain curves, and employs a newly defined scalar quantity, called the small strain stiffness factor, to determine the shear stiffness at an arbitrary stress-reversal state. Thirdly, within the frameworks of elastoplastic theory and the critical state soil mechanics, an elastoplastic stress-reversal surface model is developed for sands. For a monotonic loading process, a double-parameter hardening rule is proposed to account for the coupled compression-shear hardening mechanism. For a cyclic loading process, a new kinematic hardening rule of the loading surface is elaborately designed in stress space, which can be conveniently incorporated with the stressreversal method. Finally, the stress-reversal surface model is used to simulate some laboratory triaxial tests on two sands, including monotonic loading tests along conventional and special stress paths, as well as drained cyclic tests with regular and irregular shearing amplitudes. A more systematic comparison between the model simulations and relevant test data validates the rationality and capability of the model, demonstrating its distinctive performance under irregular cyclic loading condition.

Damping plays an important role in the design of offshore wind turbine structures. The hysteretic damping of the seabed soil represents the energy dissipation caused by the soil-particle interaction and the nonlinear behavior of the soil under cyclic loading. However, the effect of sand damping on the lateral response of the monopile foundation of an offshore wind turbine is still unclear. In this paper, the effect of soil hysteretic damping on the lateral dynamic response of a monopile foundation in a sandy seabed is investigated using a subplastic soil constitutive model. The constitutive model response at the foundation level is verified by comparing the monotonic and cyclic responses of the monopile with the results of the 1g model test. The results show that when soil hysteretic damping is present in the monopile-soil system, the energy dissipation in the soil reduces the stress accumulation in the soil, resulting in a reduction in the bending moment and horizontal displacement of the monopile, compared with the case without soil hysteretic damping. The results are crucial for optimizing the monolithic design of offshore wind turbine structures.