Constitutive models of sands play an essential role in analysing the foundation responses to cyclic loads, such as seismic, traffic and wave loads. In general, sands exhibit distinctly different mechanical behaviours under monotonic, regular and irregular cyclic loads. To describe these complex mechanical behaviours of sands, it is necessary to establish appropriate constitutive models. This study first analyses the features of hysteretic stressstrain relation of sands in some detail. It is found that there exists a largest hysteretic loop when sands are sufficiently sheared in two opposite directions, and the shear stiffness at a stress-reversal point primarily depends on the degree of stiffness degradation in the last loading or unloading process. Secondly, a stress-reversal method is proposed to effectively reproduce these features. This method provides a new formulation of the hysteretic stress-strain curves, and employs a newly defined scalar quantity, called the small strain stiffness factor, to determine the shear stiffness at an arbitrary stress-reversal state. Thirdly, within the frameworks of elastoplastic theory and the critical state soil mechanics, an elastoplastic stress-reversal surface model is developed for sands. For a monotonic loading process, a double-parameter hardening rule is proposed to account for the coupled compression-shear hardening mechanism. For a cyclic loading process, a new kinematic hardening rule of the loading surface is elaborately designed in stress space, which can be conveniently incorporated with the stressreversal method. Finally, the stress-reversal surface model is used to simulate some laboratory triaxial tests on two sands, including monotonic loading tests along conventional and special stress paths, as well as drained cyclic tests with regular and irregular shearing amplitudes. A more systematic comparison between the model simulations and relevant test data validates the rationality and capability of the model, demonstrating its distinctive performance under irregular cyclic loading condition.

Consolidated-drained true triaxial tests with constant b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b$$\end{document} values were performed on normally consolidated cross-anisotropic kaolin clay. Isotropic stress probes were incorporated into these true triaxial tests to study the orientations of plastic strain increment vectors and positioning of the plastic potential surface at different levels of shearing. An isotropic compression test was also performed to characterize the cross-anisotropic response of the clay. Pronounced cross-anisotropy was observed in the K0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{0}$$\end{document} consolidated kaolin clay during shear, particularly when the major and minor principal stresses were perpendicular and parallel to the axis of material symmetry, respectively. A simple rotational kinematic hardening mechanism incorporated into the single hardening constitutive model for soil has been found to fairly accurately simulate the evolution of anisotropy in the form of expansion and rotation of the yield and plastic potential surfaces during true triaxial shearing.

In cold regions, the frozen soil-rock mixture (FSRM) is subjected to cyclic loading coupled with freeze-thaw cycles due to seismic loading and ambient temperature changes. In this study, in order to investigate the dynamic mechanical response of FSRM, a series of cyclic cryo-triaxial tests were performed at a temperature of -10 degrees C on FRSM with different coarse-grained contents under different loading conditions after freeze-thaw cycles. The experimental results show that the coarse-grained contents and freeze-thaw cycles have a significant influence on the deformation properties of FSRM under cyclic loading. Correspondingly, a novel binary-medium-based multiscale constitutive model is firstly proposed to describe the dynamic elastoplastic deformation of FSRM based on the coupling theoretical framework of breakage mechanics for geomaterials and homogenization theory. Considering the multiscale heterogeneities, ice-cementation differences, and the breakage process of FSRM under external loading, the relationship between the microscale compositions, the mesoscale deformation mechanism (including cementation breakage and frictional sliding), and the macroscopic mechanical response of the frozen soil is first established by two steps of homogenization on the proposed model. Meanwhile, a mixed hardening rule that combines the isotropic hardening rule and kinematic hardening is employed to properly evaluate the cyclic plastic behavior of FSRM. Finally, comparisons between the predicted results and experimental results show that the proposed multiscale model can simultaneously capture the main feature of stress-strain (nonlinearity, hysteresis, and plastic strain accumulation) and volumetric strain (contraction and dilatancy) of the studied material under cyclic loading.

The soil surrounding bucket foundations that are subjected to vertical cyclic loading would become softened but not consolidated. This would reduce the uplift resistance and even cause foundation failure. The paper firstly investigates the development, especially the dissipation of excess pore pressure and base suction (the suction between the bucket lid and soil) under vertical cyclic loading through 1 g model tests. The test results demonstrate that although base suction can bear 54 % of the uplift resistance of the bucket foundation at the beginning, the upward movement of foundation causes cracks at the soil surface, which accelerates excess pore pressure dissipation and leads to faster foundation failure. Therefore, the base suction should not be considered in the foundation design under long-term cyclic uplift loading. Then, an amended kinematic hardening model that can consider the strain softening effect of soil is employed to obtain the uplift resistance under vertical monotonic and cyclic loadings for various soil softening parameters and cyclic load level (the ratio of cyclic mean load to the monotonic ultimate uplift resistance). Through extensive fatigue analyzes with tens of thousands or even hundreds of thousands of cyclic loadings in each analysis, it is concluded that the fatigue cyclic number increases as the cyclic load level decreases or softening parameters (xi 95 and delta rem) increase. A prediction formula of fatigue curve of bucket foundation is proposed and verified to predict the fatigue cyclic number. The prediction error is within 10 %, and the formula can provide a convenient reference for the design of bucket foundation.

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction. This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of con fining/ consolidation pressures. The issue stems from the pressure independent hardening law in the classical deviatoric hardening model. To overcome this problem, we propose a re fined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations. Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various con fining/consolidation pressure conditions for both dense and loose sands. Furthermore, to examine the importance of the improved deviatoric hardening model, it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures. It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials. (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 license (http://creativecommons.org/licenses/ by/4.0/).