Seismic activity often triggers liquefaction in sandy soils, which coupled with initial vertical tensile loads, poses a significant threat to the stability of suction bucket foundations for floating wind turbines. However, there remains a notable dearth of studies on the dynamic response of these foundations under combined seismic and vertical tensile loads. Therefore, this study developed a numerical method for analyzing the dynamic response of suction bucket foundations in sandy soils under such combined loading conditions. Through numerical simulations across various scenarios, this research investigates the influence of key factors such as seismic intensity, spectral characteristics, as well as the magnitude and direction of tensile loads on the seismic response of suction buckets. The results revealed that the strong earthquake may cause the suction bucket foundation of floating wind turbines to fail due to excessive vertical upward displacement. This can be attributed to that the accumulation of excess pore water pressure reduces the normal effective stress on the outer wall of bucket, and consequently decreases the frictional resistance of bucket-soil interface. Additionally, the above factors significantly influence both the vertical displacement of the suction bucket and the development of pore pressure in the surrounding soil. The findings can provide valuable insights for the seismic safety assessment of suction bucket foundations used in tension-leg floating wind turbines.

A series of undrained cyclic torsional shear tests were conducted to investigate the effect of cyclic loading frequency on the liquefaction characteristics of saturated sand using the hollow cylinder apparatus. The test results show that the dilative and contractive tendencies of various saturated sands are not only related to the physical properties of sand, but also affected by loading frequency. Under low-frequency loading, the saturated sand has a dilative behaviour, excess pore water pressure fluctuates after initial liquefaction and soil maintains the ability to resist liquefaction to some extent after the initial liquefaction. The liquefaction mode in terms of stress-strain relationship generally performs as the cyclic mobility. However, under the high-frequency loading, the saturated sand has a contractive behaviour, excess pore water pressure generally keeps stable after the initial liquefaction. The liquefaction mode in terms of stress-strain relationship generally exhibits as cyclic instability. The deformation caused by low-frequency loading is significantly larger compared with that caused by high-frequency loading. At higher loading frequencies, the phase transformation stress ratio increases with the increase of loading frequency, and gradually approaches the failure stress ratio.

To determine the effects of root volume density on the mechanical behaviour of sand, drained and undrained triaxial compression tests were conducted on sand with root volume densities of 0.8%, 1.2%, 1.6%, 2.0%, and 2.4% under different confining pressures. Higher root content formed a denser and more uniform root network in the soil, enabling more roots to mobilize tensile stress, share external loads, and limit volumetric deformation. This enhanced the root-soil composite strength, reduced volumetric strain under drained conditions, and decreased excess pore water pressure under undrained conditions. The roots made a more pronounced contribution to the soil shear strength under lower confining pressures and undrained conditions. Specifically, with increasing confining pressure, the increment in the inherent soil strength far exceeded that in the additional strength provided by the roots. Under undrained conditions, the roots enhanced the soil strength by bearing part of the external loads and preventing the development of excess pore water pressure. Furthermore, the critical state line of a root-soil composite depended on the stress path. Since roots are non-granular materials and their mechanical reinforcement effect varies under different stress paths. Additionally, the roots enhanced liquefaction resistance of the sand by raising the initial effective stress required for triggering static liquefaction and the critical state effective stress. The greater the root volume density was, the stronger the liquefaction resistance of the sand.

The paper details some practical considerations associated with the numerical simulation of liquefaction in Wildlife site in Southern California. Two material constitutive models are implemented in the simulations: a pressure-dependent multi-yield-surface model (PDMY) and PM4Sand, both available in the OpenSees finite elements platform. Both uniaxial as well as biaxial simulations are presented in the paper. The uniaxial simulations only include the predominant horizontal shaking component while the biaxial simulations include both orthogonal horizontal shaking components. Two historical major earthquake events were simulated: the 1987 Superstition Hills and the 2010 El Mayor Cucapah earthquakes. Laboratory experimental data used for calibration of the material models was obtained from historical data published in the 1980's. This data is particularly valuable since they correspond to intact (undisturbed) samples extracted from Wildlife site about two years before occurrence of the 1987 earthquake. In all the simulations, the models were able to capture salient features of the deposit's behavior, such as the magnitude of surface accelerations, and dilative behavior of the soil. However, the excess pore water pressure rises earlier than what the site recordings indicates. This may be attributed to the fact that the constitutive models do not consider the concept of volumetric threshold shear strain below which no excess pore water pressure is generated during cyclic shear loading. It was also found that there was a significant overestimation of the excess pore pressure for the 2010 El Mayor Cucapah earthquake simulations. This may be attributed to the effect of the site shaking history which increased the site resistance to liquefaction. This added resistance was not reflected by the numerical model since it was calibrated with samples extracted about 25 years before the 2010 earthquake.

The mechanical response of sand is affected by the axial strain accumulated during undrained cyclic triaxial loading tests. However, the large deformation that occurs during the post-liquefaction stage is difficult to measure using testing apparatus. To address this limitation, this research utilizes the numerical method of DEM with non-spherical particles to simulate the undrained cyclic triaxial loading test on clean sand material. The validity of DEM is confirmed through laboratory test. A four-stage scheme for the development of axial strain in the liquefaction process is proposed and verified by analyzing the deformation features of sand specimens with different densities. Meanwhile, the macroscopic behavior is also described in conjunction with microscopic characteristics of sand particles, such as coordination number, force chain network and anisotropy degree of contact normal, which are calculated using DEM. In addition, the central value of variating axial strain at each cycle is analyzed to determine its variation feature via loading cycle. Due to the capability of DEM in describing the microscopic behavior of soil particle aggregation, it is found that the difference in the proposed four-stage scheme between compression and extension sides is the main cause of the central value of axial strain shifting monotonically.