Offshore wind turbines (OWTs) are subjected to prolonged external loading, including loads induced by wave action. The soil undergoes bi-directional coupled shear, due to this low-frequency and long-duration loading, the cumulative deformation of the offshore foundation is observed to increase, which poses a threat to the functional reliability of the offshore wind turbines. The soil around the piles is distributed with clay layers. Due to the complex mechanical properties of clay, bi-directional cyclic loading tests are performed to research the drainageinduced deformation characteristics of clays in this paper. Based on these test results, the variation of hysteresis loops of stress-strain, resilient modulus, and the cumulative strain are found to exhibit a strong correlation with both the cyclic stress level and the confining pressure. The stress-strain hysteresis loops and resilient modulus have significantly different trends at higher or lower cyclic stress levels. Then an empirical model that uniformly reflects the strain-hardening and softening characteristics, and an empirical model reflects the characteristics of cumulative strain development in soils is established. Finally, the performance of the permanent cumulative strain prediction model is assessed based on the in-situ test findings from the clay foundation.

Long-term cyclic loading applied to clay at stress levels lower than the critical cyclic stress leads to soil deformation without inducing damage. The Monismith model is well-known for its simplicity and ability to describe the trend of cumulative plastic strain under cyclic loading. However, the simulated cumulative plastic strain increases indefinitely with the number of cycles until damage occurs. At lower cyclic stress levels, the cumulative plastic strain tends to be stabilized with an increasing number of cycles, ultimately limits the applicability of the model. To address this issue, a series of axial-torsional bi-directional cyclic loading tests are conducted on saturated clay using a hollow cylinder torsional shear apparatus. An empirical three-parameter mathematical prediction model is proposed by analyzing the development of cumulative generalized shear strain based on test results. The relationships of model parameters a with plasticity index, frequency, generalized shear stress, and mean effective stress; b with plasticity index, and c with frequency and plasticity index are presented as functional expressions. Finally, the predicted results of the empirical model are compared with test results to verify its effectiveness, providing a basis for calculating cumulative deformation in clay under long-term low cyclic stress levels.