This paper presents a rigorous, semi-analytical solution for the drained cylindrical cavity expansion in transversely isotropic sand. The constitutive model used for the sand is the SANISAND-F model, which is developed within the anisotropic critical state theory framework that can account for the essential fabric anisotropy of soils. By introducing an auxiliary variable, the governing equations of the cylindrical expansion problem are transformed into a system of ten first-order ordinary differential equations. Three of these correspond to the stress components, three are associated with the kinematic hardening tensor, three describe the fabric tensor, and the last one represents the specific volume. The solution is validated through comparison with finite element analysis, using Toyoura sand as the reference material. Parametric analyses and discussion on the impact of initial void ratio, initial mean stress level, at-rest earth pressure coefficient and initial fabric anisotropy intensity are presented. The results demonstrate that the fabric anisotropy of sand significantly influences the distribution of stress components and void ratio around the cavity. When fabric anisotropy is considered, the solution predicts lower values of radial, circumferential and vertical stresses near the cavity wall compared to those obtained without considering fabric anisotropy. The proposed solution is expected to enhance the accuracy of cavity expansion predictions in sand, which will have significant practical applications, including interpreting pressuremeter tests, predicting effects of driven pile installation, and improving the understanding of sand mechanics under complex loading scenarios.

In geotechnical engineering, the development of efficient and accurate constitutive models for granular soils is crucial. The micromechanical models have gained much attention for their capacity to account for particle-scale interactions and fabric anisotropy, while requiring far less computational resources compared to discrete element method. Various micromechanical models have been proposed in the literature, but none of them have been conclusively shown to agree with the critical state theory given theoretical proof, despite the authors described that their models approximately reach the critical state. This paper modifies the previous CHY micromechanical model that is compatible with the critical state theory based on the assumption that the microscopic force-dilatancy relationship should align with the macroscopic stress-dilatancy relationship. Moreover, under the framework of the CHY model, the fabric anisotropy can be easily considered and the anisotropic critical state can be achieved with the introduction of the fabric evolution law. The model is calibrated using drained and undrained triaxial experiments and the results show that the model reliably replicates the mechanical behaviors of granular materials under both drained and undrained conditions. The compatibility of the model with the critical state theory is verified at both macroscopic and microscopic scales.

Anisotropic soils exhibit complex mechanical behaviours under various loadsing conditions, e.g., reversible dilatancy, three-dimensional failure strength, fabric anisotropy, small-strain stiffness, cyclic mobility, making it difficult to comprehensively capture these characteristics within a single constitutive model. Failure to capture anisotropic soil behavious may result in poor predictions in geotechnical engineering. Hence, to provide a unified prediction for the mechanical responses of anisotropic sand and clay under both monotonic and cyclic loading conditions, a fabric-based anisotropic constitutive model, i.e., the CASM-CF, is developed within the framework of the standard Clay and Sand Model (CASM) in this paper. Effects of small-strain stiffness and anisotropic elasticity are incorporated into the stiffness matrix to capture the stiffness variation over a wide strain range and reversible dilation. The fabric tensor defined by particle orientation and its evolution law are integrated into the CASM-CF model through the Anisotropic Transformed Stress (ATS) method. The plastic modulus is modified by considering cyclic loading history and stress reverse to better predict the mechanical responses of soils when subjected to cyclic loadings. The newly proposed model is employed to predict the mechanical behaviours of clay and sand under various strain scales and stress paths, including monotonic, cyclic, proportional, and non-proportional loading conditions, in the literature. Conclusions can be drawn that the model performs satisfactorily under various stress paths, and it has the potential to be used in the analysis of practical geotechnical applications of wide range.

The stress state and density of soil have been considered as the key factors to determine the liquefaction resistance. However, the results of seismic liquefaction case histories, laboratory tests and centrifuge model tests show that the fabric characteristics also influence liquefaction resistance, even more significantly than the contributions of stress state and density. In this study, anisotropic specimens with different consolidation histories were prepared using the 3D Discrete Element Method (DEM) to investigate the influence of fabric characteristics on the mechanical behavior of granular materials and the underlying mechanisms. The simulations revealed that under monotonic shear conditions, horizontally anisotropic specimens exhibited strain hardening and dilatancy characteristics, as well as higher peak strength. Under cyclic shear condition, the normalized liquefaction resistance of the specimens showed a strong linear relationship with the degree of anisotropy, independent of confining pressures and density. Microscopic results indicate that the fabric arrangement aligned with the loading direction leads to the evolution of the mechanical coordination number and average contact force in a manner favorable to resisting loads, which is the underlying mechanism influencing macroscopic mechanical properties. Additionally, the evolution patterns of contact normal magnitude and angle in anisotropic granular materials under cyclic loading conditions were also analyzed. The results of this study provided a new perspective on the macroscopic mechanical properties and the evolution of the microstructure of granular soils under anisotropic conditions.

Macro- and micromechanical interactions between the geogrid and granular aggregates considering particle shape effects are essential for the performance of reinforced soil structures under cyclic normal loading (CNL). Crushed limestone and spherical granular media were mixed to obtain samples with different overall regularities (OR = 0.707, 0.774, 0.841, 0.908, and 0.975). Direct shear tests under CNL were conducted at various overall regularities, normal loading frequencies, and waveforms. Consistent with experiment tests, a discrete-element method (DEM) simulation was performed, incorporating authentic particle shapes obtained through three-dimensional (3D) scanning technology. The results showed that the macroscopic interface shear strength and volume change decreased with an increase in the overall regularity and normal loading frequency. The interface shear strength and deformation under the square waveform are bound to be higher than that under other waveforms. The coordination number, porosity, and fabric anisotropy were used to explain the macroscopic interface shear behavior in relation to the overall regularity. A higher coordination number and stronger contact force were observed with a decrease in the overall regularity. As the overall regularity decreased, the interface integrity and stability became stronger, with the result that the reinforced soil structure can withstand a larger principal stress deflection. Through experimental and DEM analyses, the underlying explanation for the effect of particle shape on the mechanical interaction of reinforced soil was revealed.

For many solids, irreversible deformation is often accompanied by changes in the internal structure, impacting the reversible responses, a phenomenon termed elasto-plastic coupling. This coupling has been observed experimentally in various geomaterials, including clayey and sandy soils, as well as hard and soft rocks. Fabric anisotropy, which characterizes the internal structure, is a distinct feature of soils and significantly influences both reversible and irreversible behaviors. In this study, we adopted a coupling formulation based on the framework of anisotropic critical state theory (ACST) to describe the anisotropic elasto-plastic coupling response of soils. The formulation incorporates a deviatoric fabric tensor F, which consistently quantifies the internal structure of soils in both reversible and irreversible range, into a hyperelastic formulation and a plastic model, respectively. A novel evolution rule of F, defined based on the current stress ratio and plastic strain, is proposed, where the direction gradually aligns with the loading direction and the norm achieves different asymptotic values depending on the applied loading paths. This allows for the representation of evolved anisotropy effects on elasticity, dilatancy and strength simultaneously, providing a natural description of elasto-plastic coupling. Within this coupling framework, any anisotropic model within ACST can serve as the plastic platform for developing the elasto-plastic coupling models with anisotropic hyperelasticity. Herein, a bounding surface plastic model is utilized for illustration. The proposed model's performance is demonstrated by especially comparing simulated results to test data on evolving elastic stiffness ratios and overall elastoplastic responses under varying monotonic and cyclic loading conditions.

This paper presents a comprehensive study on the evolution of the small-strain shear modulus (G) of granular materials during hydrostatic compression, conventional triaxial, reduced triaxial, and p-constant triaxial tests using 3D discrete element method. Results from the hydrostatic compression tests indicate that G can be precisely estimated using Hardin's equation and that a linear correlation exists between a stress-normalized G and a function of mechanical coordination number and void ratio. During the triaxial tests, the specimen fabric, which refers to the contact network within the particle assembly, remains almost unchanged within a threshold range of stress ratio (SR). The disparity between measured G and predicted G, as per empirical equations, is less than 10% within this range. However, once this threshold range is exceeded, G experiences a significant SR effect, primarily due to considerable adjustments in the specimen's fabric. The study concludes that fabric information becomes crucial for accurate G prediction when SR threshold is exceeded. A stiffness-stress-fabric relationship spanning a wide range of SR is put forward by incorporating the influences of redistribution of contact forces, effective connectivity of fabric, and fabric anisotropy into the empirical equation.

True triaxial and hollow cylinder tests are among the best alternatives to explore the effects of stress paths oriented along different Lode angles on soil behavior. However, those experiments are not easy to conduct in the laboratory, especially for cyclic loading. This study investigates the undrained cyclic behavior of granular soils under true triaxial loading conditions using the discrete element method (DEM) coupled with fluid method (CFM). Numerical specimens with elongated particles oriented along three different bedding planes and in an isotropic condition were prepared and subjected to constant volume cyclic loading. Loading direction effects on the liquefaction potential were considered, applying the deviatoric stress amplitude along different Lode angles. The impact of initial fabric orientation and stress anisotropy on the micro- and macro-scale response of particulate assemblies was intensively studied. The results show the significant effect of the Lode angle on the liquefaction susceptibility and inclination of the phase transformation line of granular assemblies. It can be concluded that particulate assemblies become more prone to the onset of liquefaction by alternating the Lode angle. The inherent anisotropy and Lode angle influence the number of cycles to reach liquefaction, the slope of the phase transformation line, and the failure line.

Understanding the response of sand to complex loading conditions is vital for practical geotechnical engineering. Circular rotational shear is a special stress path where the magnitudes of three principal stresses vary following a circular stress trajectory in the it-plane with their directions fixed. Although experimental studies under such stress paths are limited, the discrete element method appears to be an appealing approach to examine the response of granular materials to varying complex loading paths in numerical virtual tests. This study presents comprehensive numerical simulations of granular samples subjected to a circular stress path under varying conditions, including samples prepared with different bedding-plane angles and densities and subjected to different stress ratios. Both macroscopic and microscopic behaviors are presented and interpreted. A contactnormal-based fabric tensor is adopted in a detailed analysis to measure the internal structure of the granular assembly. The fabric, strain, and strain increment tensors are decomposed with respect to the stress tensor, and the evolutions of these components are presented along with the key influential factors. The results obtained in this study provide useful physical insight for the development of constitutive models for granular soils under general loading conditions.

With the acceleration of urbanization, the stability of the foundation is being more crucial to the performance and service of the superstructure. As our understanding of the factors influencing soil's physical and mechanical behavior deepens, it becomes increasingly challenging for traditional limit equilibrium and limit analysis methods to accurately consider the complex factors affecting foundation stability, such as initial fabric anisotropy caused by the particle morphology and geological deposition in sand. Although some scholars had used advanced constitutive models in the finite element method (FEM) to investigate the influence of initial fabric anisotropy on mechanical responses of foundations, this approach failed to reveal the microscopic information underlying the shear failure of sandy soil foundations. In this study, the influence of the initial fabric anisotropy of sandy soil on the ultimate bearing capacity and shear failure mode of shallow foundation is studied using the hierarchical FEM and discrete element method (DEM) coupling analysis method. Four representative volume elements (RVEs) with varying initial bedding plane angles are constructed in DEM for characterizing different initial fabric anisotropies, and the specific stress-strain information of DEM RVEs is directly passed into the corresponding Gauss points in FEM to replace the conventional constitutive model. Numerical results show that the initial fabric anisotropy affects the ultimate bearing capacity and shear failure mode of shallow foundations significantly, and the corresponding micromechanical behaviors at different local Gauss points have been explored, which advances our understanding of the micromechanisms underlying the progressive shear failure of sandy soil foundations significantly.