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.

The main objective of this study was to investigate the response of uniform sand under constant volume (i.e., undrained) conditions and how it is influenced by the initial anisotropy induced in the soil fabric due to preshearing stress history. The experimental program explored a range of parameters, including stress-strain response, tendency to volume change, phase transformation, flow instability, noncoaxiality between stress and strain rate, and the critical state line. To induce initial anisotropy, samples were presheared along different directions and subsequently tested using an Swedish Geotechnical Institute (SGI)-type bidirectional direct simple shear apparatus. The testing program focused on the effects of initial anisotropy that were induced by preshearing, resulting from the application of initial shear stress in various directions relative to the subsequent shearing direction. To interpret the variations of stresses within the samples, Budhu's approach for stress state determination in simple shear specimens was adopted. The results demonstrate that the stress-strain behavior and global volume change tendency of the soil are heavily influenced by the magnitude and direction of the preshearing stress history. Furthermore, the study reveals that the effects of stress history significantly diminish at large shear strains as the samples approach the critical state.

The naturally deposited soil usually does not consist of pure coarse or fine-grained soil but of a mixture of both. The mechanical behaviour of a saturated fine sand mixed with varying amounts of low-plastic fines was evaluated by monotonic as well as high-cyclic triaxial tests. The test results were used to conclude on the effect of fines content on the critical state, phase transformation line, secant Young's modulus, the residual strain accumulation as well as strain amplitude during drained cycles of the mixtures in relation to the global void ratio as well as to the equivalent void ratio. It was found that while the choice of void ratio definition is important for the uniqueness of the critical void ratio, both approaches can be used as state variables for the phase transformation line. However, some seemingly contradictive results are found from the drained high-cyclic tests. Eventhough, an increase of the residual strain accumulation with decreasing fines content compared at the same initial equivalent void ratio is rendered by the laboratory data, a unique and on fines content independent relationship between eacc could be established only with respect to the initial global void ratio.

Various constitutive formulations have been developed over the years to reproduce the cyclic resistance of sands. A common challenge for existing models is the accurate simulation of the cyclic strength of sands for a wide range of initial conditions and different cyclic stress levels when adopting a single calibration. Many liquefaction models tend to overpredict the resistance of the soil under large-amplitude loading, while underestimating the strength at low-amplitude cyclic shearing. This manifests itself in slopes of simulated cyclic resistance ratio curves (CRR-curves) which are steeper than experimental studies indicate. This paper provides a discussion on the effects of large-amplitude and low-amplitude cyclic shearing on a granular material based on micromechanical and experimental investigations presented in the literature. A constitutive model with a shear-history threshold is proposed, which accounts for a shift of the apparent angle of phase transformation under cyclic loading. In addition, a novel expression for a deviatoric fabric tensor is introduced to describe the evolution of shear-induced fabric anisotropy while a soil is dilating and contracting. Combining these two features in one formulation within the bounding surface plasticity framework enables an accurate prediction of cyclic strength of sands under a wide range of cyclic stress ratios.

This study presents a novel formulation for incorporating anisotropy into the generalized plasticity constitutive model. Generalized plasticity is a hierarchical framework allowing for extensibility, in order to encompass new phenomena and improve its predictive capabilities. Anisotropy formulation is based experimentally on the phase transformation state and considers explicitly the direction of the maximum principal stress and the magnitude of the intermediate principal stress, through an anisotropy state variable that contributes to the state parameter. Additionally, the model incorporates the fabric using an evolving fabric variable that reflects initial fabric due to sample preparation method for granular soils. The formulation is simple and introduces three constitutive parameters, allowing for straightforward implementation into the constitutive model and direct application in finite element analysis. The model is validated with undrained triaxial tests conducted on Toyoura sand, covering a wide range of initial conditions with a unique set of constitutive parameters, and yielding overall satisfactory results despite some limitations.