The offshore wind turbines (OWT) are subjected to cyclic loads, such as ocean waves and wind, over extended periods. The soil surrounding the pile experiences bi-directional cyclic shear. As a result of the low-frequency and long-term loading in the pile-soil interaction, the cumulative deformation of pile foundation increases, posing a risk to the operational safety of wind turbine system. The soil around the piles is distributed with soft clay and clay layers. To study the cumulative deformation properties of clay under complex stress states. A series of tests are conducted, the variation of resilient modulus under different cyclic stress levels and confining pressures is analyzed based on test results. Then an empirical model uniformly reflecting strain-hardening and strainsoftening properties of clay is proposed. The variations of model parameters are investigated. Then the established empirical model is used to modify the maximum elastoplastic modulus at each unloading within the bounding surface constitutive model, a parameter reflecting the magnitude and rate of strain accumulation is also introduced. This method is characterized by a simple expression and requires fewer model parameters. Finally, the predicted results of modified constitutive model are compared with test results to verify the validity of the established model.

To investigate the long-term stability of deep rocks, a three-dimensional (3D) time-dependent model that accounts for excavation-induced damage and complex stress state is developed. This model comprises three main components: a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state, a quantitative relationship between critical irreversible deformation and complex stress state, and evolution characteristics of strength parameters. The proposed model is implemented in a self-developed numerical code, i.e. CASRock. The reliability of the model is validated through experiments. It is indicated that the time-dependent fracturing potential index (xTFPI) at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage. The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress, thereby highlighting the 3D stress-dependent characteristic of the model. Finally, the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed. (c) 2024 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).