The stability of geotechnical structures after an earthquake is primarily determined by the residual strength of surrounding soils that have not fully liquefied. This research employs the discrete element method (DEM) to study the undrained post-cyclic shear behaviour of sand under triaxial conditions, focusing on the effect of varying degrees of liquefaction (LD) simulated by subjecting the samples to different lengths of cyclic loading. Different types of cyclic loading, i.e. symmetric (fully reversal), partially reversal, and non-reversal ones, as well as the effect of sample density, have been considered. The results indicate that the samples under fully or partially reversal cyclic loading eventually liquefied, displaying a cyclic mobility failure mode. In contrast, samples under non-reversal cyclic loading develop plastic strain accumulation (PSA) failure without liquefaction. The post-cyclic shear stiffness of the samples is affected by both LD and the type of cyclic loading. For samples under reversal cyclic loading, the post-cyclic shear stiffness decreases as LD increases. Notably, the liquefied samples (LD = 1) initially exhibit near-zero stiffness during post-liquefaction shear until highly anisotropic force chains are formed along the loading direction, with their buckling leading to stiffness recovery. The length of the low-stiffness stage is influenced by the static shear stress and the relative density of the sample, which determines the rate of anisotropy accumulation during cyclic loading. The onset and completion of stiffness recovery are marked by a peak in anisotropy and an abrupt increase in effective anisotropy, respectively. For samples under non-reversal cyclic loading, the post-cyclic shear stiffness initially decreases with the increase in LD but increases at higher LDs due to the significant anisotropy developed during the cyclic loading stage.

Subgrades may be subjected to intermittent cyclic loads such as traffic loads. Under these loading conditions, excess pore water pressure can accumulate in clayey soils during cyclic loading period and dissipate during resting time. The deformation behaviour of clayey soil after reconsolidation process may be different from that under consecutive cyclic loading. A series of undrained cyclic triaxial tests, including reconsolidation process between cyclic loading stages, were performed on kaolin clay. The axial strain accumulation, excess pore water pressure accumulation, deviatoric stress-strain loop and resilience modulus under different cyclic stress ratios, initial confining pressures and degrees of reconsolidation were discussed and presented. Test results show that the reconsolidation process has significant effects on the deformation characteristics of clayey soil. The coupling effects of change of void ratio and effective mean stress result in a non-monotonic relationship between normalised total axial strain and degree of reconsolidation. In addition, an increase in the degree of reconsolidation leads to an increase in the normalised excess pore water pressure increment during 2nd cyclic loading stage, regardless of cyclic stress ratio and initial confining pressure. Furthermore, the steady resilience modulus at the end of each cyclic loading stage depends on the effective cyclic stress ratio and initial confining pressure, irrespective of reconsolidation process.

The cyclic loading of foundation structures in sand leads to an accumulation of plastic deformations in the structures. For shallow foundations of high and slender structures such as wind energy converters (WECs), an accumulation of the plastic rotations is expected under cyclic eccentric loading that is imposed by wind loads, which could be crucial for the proof of serviceability. A practical approach to predict the behavior of shallow foundations under high-cycle eccentric loading is under research. In this paper, a numerical approach, the cyclic strain accumulation method (CSAM), which has been validated for cyclically loaded monopiles, is adopted for shallow foundations under eccentric cyclic loading. Modifications to the CSAM are described, which are necessary to apply it to shallow foundations. The results that are gained with the modified method are compared with a medium-scale model test, in which the deformations of a footing with a diameter of 2.0 m under eccentric one-way cyclic loading were investigated. It can be concluded that the CSAM can make realistic predictions and shows satisfying agreement with the measured cyclic behavior. Although more experiments are needed to finally validate the method, the CSAM could be a promising numerical approach to account for the cyclic behavior of shallow foundations under eccentric cyclic loading in sand.

Although the mechanical response of granular materials strongly depends on the interplay between their anisotropic internal structure (fabric) and loading direction, such coupling is not explicitly considered in existing high-cycle experimental datasets and models. High-cycle experiments on granular specimens specifically prepared with various fabric orientations are presented. It is found that the high-cycle strain accumulation behavior can change remarkably, from shakedown to ratcheting, when the fabric orientation deviates more from the loading direction. Inspired by the experimental observations, a fabric-dependent anisotropic high-cycle model is proposed, by proper recasting of an existing model formulated within Critical State Theory, into the framework of Anisotropic Critical State Theory. The model explicitly accounts for the fabric evolution, which is linked to plastic modulus, dilatancy and kinematic hardening rules. The model can quantitatively reproduce the high-cycle strain accumulation (i.e., shakedown and ratcheting) under drained conditions, as well as pre-liquefaction and post-liquefaction responses granular materials having widely ranged fabric anisotropy, densities and cyclic loading types using a unified set of constants. It exhibits a unique feature of simulating the distinct high-cycle strain accumulation and liquefaction of granular material with various fabric anisotropy, while the existing high-cycle models treat them equally. The successful reproduction of the anisotropic sand element response under high-cycle drained and undrained conditions makes it possible to perform whole life analysis of various foundations on granular soil subjected to high-cycle loading events.

This study investigates the effect of a stress state change at an intermediate stage during cyclic loading on the drained cyclic deformation of soil using Discrete Element Method (DEM) simulations. Drained cyclic triaxial simulations were conducted on an assembly of irregularly shaped particles, with the stress state shifting along different stress paths at an intermediate stage of cyclic loading. The analysis of the macro- and microscopic responses reveals a link between the cyclic stress-dilatancy behaviour and the anisotropy of the granular assembly. In the simulations without the stress state change or with a stress ratio increase, the strain accumulation direction aligns with the prediction of the Modified Cam Clay (MCC) flow rule; and the strain accumulation is faster at higher stress ratios when the contact distribution is more anisotropic. However, when the particle assembly experiences a stress ratio decrease during cyclic loading, the subsequent strain accumulation direction deviates from the MCC flow rule, and strains accumulate more rapidly at lower stress ratios when the contact distribution is nearly isotropic. A tentative explanation is proposed to explain the altered strain accumulation direction after the stress ratio decrease.

Changing the deviatoric and spherical stresses could affect the accumulative deformation behaviour of soils under cyclic loading. Drained cyclic triaxial loading tests were performed on saturated sand to study the dependence of cyclic loadinginduced axial and volumetric strain accumulations on changing the deviatoric and spherical stresses in between loading cycles. The change in the stresses was simulated by changing cell pressure and axial load along different stress paths. The variation of axial and volumetric strain accumulations before and after changing the stresses is compared and discussed. It is found that changing the stresses could have different impacts on the axial and volumetric strain accumulations, as the accumulations are affected by different mechanisms. The axial strain accumulation after changing the stresses is affected by the average stress ratio and precedent stress history. The volumetric strain accumulation is hardly affected by changing the stresses unless an increase in the average stress ratio is caused. Both axial and volumetric strain accumulations show independence on the stress path of the disturbance. For the samples with decreasing average stress ratio, the strain accumulation direction after changing the stresses cannot be fully described using Modified Cam Clay flow rule.