Laboratory experiments have shown that the proportional shearing of granular materials along arbitrary strain path directions will lead to stress states that converge asymptotically to proportional stress paths with constant stress ratios. The macro- and microscopic characteristics of this asymptotic behaviour, as well as the existence of asymptotic states exhibiting a constant stress ratio and a steady strain-rate direction, have been studied using the discrete element method (DEM). Proportional shearing along a wide range of strain-rate directions and from various initial stress/density states has been conducted. The simulation results suggest that general contractive asymptotic states (except for isotropic states) do exist but may be practically unattainable. Dilative strain path simulations, on the other hand, result in continuously changing stress ratios until static liquefaction occurs, indicating the absence of dilative asymptotic states. Despite this difference, a unique relationship between the stress increments and the current stress ratio gradually emerges from all strain path simulations, regardless of strain path direction and initial stress/density conditions. At the particle scale, the granular assembly sheared along proportional strain paths exhibits a constant partition ratio between strong and weak contacts. Although general proportional strain paths are associated with changing geometric and mechanical anisotropies, the rates of change in these anisotropies for contractive strain paths are synchronised to maintain a constant ratio of their contributions to the mobilised shear strength of the material, with a higher proportion being contributed by geometric anisotropy for more dilative strain paths.

Due to the development of plastic strains, the strain path within the meridian plane deviates from the reference line corresponding to elastic state. Similarly, under true triaxial stress conditions, the strain path within the deviatoric plane deviates from the reference line corresponding to the constant Lode angle. This deviation is attributed to the plastic shear strain associated with the Lode angle. To account for these phenomena, a novel three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed to characterize the deformation behavior of sandstone. The yield and potential functions within this model incorporate parameters that vary with the plastic internal variable, enabling the evolution of the yield and plastic potential surfaces in both the meridian and deviatoric planes. The comparison between experimental data and the analytic solution derived from the constitutive model validates its reliability and accuracy. To examine the differences between yield surface and plastic potential surface, a comparison between the associated and non-associated flow rules is conducted. The results indicate that the associated flow rule tends to overestimate the dilatancy of sandstone. Furthermore, the role of Lode angle dependence in the potential function is explored, highlighting its importance in accurately describing the rock's deformation.

Offshore wind turbines are subjected to more significant wave and wind environmental loads at extreme weather conditions, making subsoil experience various loading stages with different amplitudes. To investigate the coupling effect of both cyclic shear stress ratio (CSR) and stage amplitude ratio (Ar) between normal and extreme weather conditions, a series of bi-directional simple shear tests with five different Ar and three CSR values were conducted on marine sand using the variable-direction dynamic cyclic simple shear (VDDCSS) apparatus. In the tests, soil samples were compacted under vertical stress and then sheared in undrained conditions by applying two shear stresses acting in different horizontal directions. Test results indicated that the cyclic strain, pore water pressure ratio, and cyclic strength were significantly determined by the value of stage amplitude ratios and the CSRs: at the same CSR, cyclic strains, and pore water pressure increased while cyclic strength decreased with the Ar. Comparing the test data between various cyclic stress ratios found that the CSRs can accelerate shear strains, pore pressure accumulation, and cyclic strength attenuation.