This study examines the behavior of anisotropically consolidated granular assemblies under undrained cyclic true triaxial loading paths. To achieve this, the Discrete Element Method (DEM) is conjugated with the Coupled Fluid Method (CFM) to account for fluid-solid interaction in undrained conditions. The examined loading paths include two phases: anisotropic consolidation and undrained cyclic true triaxial loading. During consolidation, samples are sheared at various Lode angles to reach a spectrum of initial static shear stress levels. In the second stage, undrained cyclic loading is applied with constant shear stress amplitudes at various Lode angle values. The results indicated that the monotonic and cyclic Lode angle, initial static shear stress, and amplitude of deviatoric stress have pronounced effects on the secant shear modulus degradation and the rate of excess pore water pressure generation of granular assemblies. In tandem with macro-scale observations, the evolution of the microstructure within assemblies is analyzed using the coordination number, redundancy index, inter-particle contact fabric tensor, and particle orientation fabric tensor. The micro-scale findings confirm that the anisotropy induced by changes in the loading direction significantly impacts the shear strength of the assemblies. Additionally, the fabric of assemblies aligns along the preferential direction corresponding to the major principal stress, influencing the dilative response.

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.

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.

The mechanical properties and envelope curve predictions of polyurethane-improved calcareous sand are significantly influenced by the magnitude and direction of principal stress. This study conducted a series of directional shearing tests with varying polyurethane contents (c = 2.5%, 5%, and 7.5%), stress Lode angles (theta sigma = -19.1 degrees, 0 degrees, 19.1 degrees, and 30 degrees), and major principal stress angles (alpha = 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees) to investigate the strength and non-coaxial characteristics of calcareous sand improved by polyurethane foam adhesive (PFA). Key findings revealed that failure strength varied significantly with the major principal stress axis direction, initially decreasing to a minimum at alpha = 45 degrees before increasing, with a 30% decrease and 25% increase observed at c = 5%. Non-coaxial characteristics between strain increment and stress directions became more pronounced, with angles varying up to 15 degrees. Increasing polyurethane content from 2.5% to 7.5% enhanced sample strength by 20% at theta sigma = -19.1 degrees and alpha = 60 degrees. A generalized linear strength theory in the pi-plane accurately described strength envelope variations, while a modified Lade criterion, incorporating polymer content, effectively predicted multiaxial strength characteristics with less than 10% deviation from experimental results. These contributions provide quantitative insights into failure strength and non-coaxial behavior, introduce a robust strength prediction framework, and enhance multiaxial strength prediction accuracy, advancing the understanding of polyurethane-improved calcareous sand for engineering applications.

The strain paths of cement stone in the deviatoric and meridian planes under the constant Lode angle loading path (true triaxial stress state) are analyzed. The amount of volumetric and shear strains first increases and then decreases with the intermediate principal stress coefficient. Owing to the generation of plastic volumetric strain and plastic shear strain in the direction of deviatoric stress, the strain path exhibits nonlinearity in the meridian planes. The deviation of the strain path from the constant Lode angle arises from the accumulation of plastic shear strain along the Lode angle direction. In the framework of fractional plasticity, a three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed, including yield function, potential function, and fractional flow rule. The yield surface evolves in both meridian and deviatoric planes, allowing the yield function to precisely characterize the stress state. Since the plus-minus sign in the flow direction of the yield surface is opposite to that in the flow direction of cement stone, a simple elliptic function incorporating Lode angle serves as the potential function. The procedure for the determination of fractional order based on the entirety of the deformation process is proposed, including variable and constant fractional order. The comparison between the experimental result and the analytical solution of constitutive model confirms its accuracy and validity. Furthermore, the difference between variable and constant fractional order on deformation is analyzed. The comparison results indicate that the variable fractional order can provide a more accurate description of deformation than the constant fractional order.

This study investigates the influence of micro -scale entities such as inherent and induced fabric anisotropy on the stress-strain behaviour of granular assemblies. In tandem with this exploration, our objective is to formulate a novel correlation that quantifies the evolution of fabric tensor across diverse loading paths. This correlation can be introduced to enhance the micro -mechanical insights in conventional constitutive models. Employing the Discrete Element Method (DEM), we simulate the drained and undrained responses of 680 transversely isotropic particulate assemblies with diverse initial fabrics and particle Aspect Ratio (AR) under true triaxial loading conditions. We consider a second -order fabric tensor based on inter -particle contact orientations to trace fabric evolution during loading. To account for fluid-solid interaction under undrained conditions, we adopted the DEM-Coupled Fluid Method (CFM). The simulation results highlight the significant influence of the Lode angle, particle shape and initial fabric on the stress-strain behaviour of granular materials, with fabric evolution primarily affected by the stress state, void ratio and particle AR. Lastly, we propose a new correlation for the quantification of the fabric tensor using a multi -layer feed -forward neural network. The satisfactory performance of the suggested correlation is demonstrated through a comparison between DEM data and predicted fabric tensor values.

A comprehensive three-dimensional elastoplastic constitutive model is presented to characterize the stress-strain behavior of cement stone under the true triaxial stress state. This constitutive model incorporates a threedimensional yield function and a three-dimensional potential function. The three-dimensional yield function is designed to accurately represent the true triaxial stress state during hardening. The three-dimensional potential function is devised to depict the plastic flow direction under true triaxial stress state. The yield and potential functions include parameters that control the shape of the deviatoric and meridian planes, and these parameters vary with the plastic internal variable. Consequently, the yield function can accurately describe the stress state, and the potential function can precisely capture the variations in plastic flow direction. Additionally, a detailed procedure for determining the parameters of the yield function and potential function is proposed based on the full deformation process. The constitutive model is presented in the form of analytical solution. The comparison of experimental data with the constitutive model confirms its accuracy and validity. A sensitivity analysis of the deviatoric and meridian parameters in the potential function is performed, shedding light on their impact on the model behavior. Furthermore, the significance of incorporating Lode angle dependence into the potential function is discussed, emphasizing its essential role in accurately capturing strain in the direction of the intermediate principal stress.

The shape of the failure locus of a material is significant for its strength predictions. Even when constitutive models include the same critical stress surface, different critical stress ratios can be predicted for an identical applied isochoric strain path. In this article, we investigate critical stress predictions of different constitutive models, which include the surface according to Matsuoka-Nakai (MN). We perform analytical investigations, true triaxial test simulations with hypoplasticity and barodesy, and discrete element modelling (DEM) simulations to investigate the friction dependency of the stress Lode angle. Our results demonstrate that in hypoplasticity, the direction of the deviatoric stress state at critical state depends solely on the direction of the applied deviatoric strain path. In contrast, in barodesy, the predictions are also dependent on the friction angle of the material. In addition, we compare these results with those obtained with a standard elastoplastic MN model. To validate this friction dependency on the stress Lode angle, we conduct DEM simulations. The DEM results qualitatively support the predictions of barodesy and suggest that a higher friction results in a higher Lode angle at critical stress state.